rational surface maps with invariant meromorphic two forms let f s dashrightarrow s be a rational self map of a smooth complex projective surface s and eta be a meromorphic two form on s satisfying f eta delta eta for some delta in mathbf c we show that under a mild topological assumption on f there is a birational change of domain psi x dashrightarrow s such that psi eta has no zeros in this context we investigate the notion of algebraic stability for f proving that f can be made algebraically stable if and only if it acts nicely on the poles of eta we illustrate this last result in the case eta frac dx wedge dy xy where we translate our stability result into a condition on whether a circle homeomorphism associated to f has rational rotation number

cramer rao lower bounds for subcarrier snr estimates over multicarrier channels considering orthogonal frequency division multiplexing transmissions analytical expressions for the cramer rao lower bounds for the subcarrier signal to noise ratio snr estimates are derived the transmitted signal is assumed to be corrupted by additive white gaussian noise on the different subcarriers the channel is assumed to be slowly time varying over the observation interval so that it can be assumed constant it will be shown that the achievable performance on subcarrier snr estimation can be significantly improved by exploiting the mutual information the same experienced noise power between the different tones

analytic invariant manifolds for sequences of diffeomorphisms abstract we obtain real analytic invariant manifolds for trajectories of maps assuming only the existence of a nonuniform exponential behavior we also consider the more general case of sequences of maps which corresponds to a nonautonomous dynamics with discrete time we emphasize that the maps that we consider are defined in a real euclidean space and thus one is not able to obtain the invariant manifolds from a corresponding procedure to that in the nonuniform hyperbolicity theory in the context of holomorphic dynamics we establish the existence both of stable and unstable manifolds and of center manifolds as a byproduct of our approach we obtain an exponential control not only for the trajectories on the invariant manifolds but also for all their derivatives

a modified algorithm for generalized discriminant analysis generalized discriminant analysis gda is an extension of the classical linear discriminant analysis lda from linear domain to a nonlinear domain via the kernel trick however in the previous algorithm of gda the solutions may suffer from the degenerate eigenvalue problem i e several eigenvectors with the same eigenvalue which makes them not optimal in terms of the discriminant ability in this letter we propose a modified algorithm for gda mgda to solve this problem the mgda method aims to remove the degeneracy of gda and find the optimal discriminant solutions which maximize the between class scatter in the subspace spanned by the degenerate eigenvectors of gda theoretical analysis and experimental results on the orl face database show that the mgda method achieves better performance than the gda method

a comparison of snr estimation techniques for the awgn channel the performances of several signal to noise ratio snr estimation techniques reported in the literature are compared to identify the best estimator the snr estimators are investigated by the computer simulation of baseband binary phase shift keying psk signals in real additive white gaussian noise awgn and baseband 8 psk signals in complex awgn the mean square error is used as a measure of performance in addition to comparing the relative performances the absolute levels of performance are also established the simulated performances are compared to a published cramer rao bound crb for real awgn and a crb for complex awgn that is derived here some known estimator structures are modified to perform better on the channel of interest estimator structures for both real and complex channels are examined

cramer rao bounds for snr estimation of oversampled linearly modulated signals most signal to noise ratio snr estimators use the receiver matched filter output sampled at the symbol rate an approach which does not preserve all information in the analog waveform due to aliasing thus it is relevant to ask whether avoiding aliasing could improve snr estimation to this end we compute the corresponding data aided da and nondata aided nda cramer rao bounds crbs we adopt a novel dual filter framework which is shown to be information preserving under suitable conditions and considerably simplifies the analysis it is shown that the crb can be substantially reduced by exploiting any available excess bandwidth depending on the modulation scheme the snr range and the estimator type da or nda

the fibonacci hamiltonian we consider the fibonacci hamiltonian the central model in the study of electronic properties of one dimensional quasicrystals and establish relations between its spectrum and spectral characteristics namely the optimal holder exponent of the integrated density of states the dimension of the density of states measure the dimension of the spectrum and the upper transport exponent and the dynamical properties of the fibonacci trace map such as dimensional characteristics of the non wandering hyperbolic set and its measure of maximal entropy as well as other equilibrium measures topological entropy multipliers of periodic orbits we also exhibit a connection between the spectral quantities and the thermodynamic pressure function as a result a detailed description of the spectral properties for all values of the coupling constant is obtained in contrast to all previous quantitative results which could be established only in the regime of small or large coupling in particular we show that the spectrum of this operator is a dynamically defined cantor set and that the density of states measure is exact dimensional this implies that all standard fractal dimensions coincide in each case we show that all the gaps of the spectrum allowed by the gap labeling theorem are open for all values of the coupling constant also we establish strict inequalities between the four spectral characteristics in question and provide the exact large coupling asymptotics of the dimension of the density of states measure for the other three quantities the large coupling asymptotics were known before

cramer rao lower bounds for nda snr estimates of square qam modulated transmissions in this paper we derive for the first time analytical expressions for the exact cramer rao lower bounds on the variance of unbiased non data aided nda signal to noise ratio snr estimators of square qam modulated signals the channel is assumed to be constant over the observation interval and the received signal is supposed to be corrupted by additive white gaussian noise awgn the derived expressions corroborate previous attempts to numerically compute the considered crlbs it will be shown that the nda crlbs differ widely from one modulation order to another especially at moderate snr levels

dynamics of bimeromorphic maps of surfaces we classify bimeromorphic self maps f x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of compact kahler surfaces x in terms of their actions f h 1 1 x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i on cohomology we observe that the growth rate of f n is invariant under bimeromorphic conjugacy and that by conjugating one can always arrange that f n f n we show that the sequence f n can be bounded grow linearly grow quadratically or grow exponentially in the first three cases we show that after conjugating f is an automorphism virtually isotopic to the identity f preserves a rational fibration or f preserves an elliptic fibration respectively in the last case we show that there is a unique up to scaling expanding eigenvector for f that is nef and that f is bimeromorphically conjugate to an automorphism if and only if 2 0 we go on in this case to construct a dynamically natural positive current representing and we study the growth rate of periodic orbits of f we conclude by illustrating our results with a particular family of examples

moment based parameter estimation and blind spectrum sensing for quadrature amplitude modulation knowing accurate noise variance and signal power is crucial to most spectrum sensing algorithms such as energy detection matched filter detection and cyclostationary detection in this paper we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing this task is non trivial without knowing the status of the primary user and we categorize the related spectrum sensing as a blind one we develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user three different parameter estimators that do not require any training are then proposed based on the moments of the received signals since the secondary user may not know the primary user s signal constellation we develop a robust approach that approximates a finite quadrature amplitude modulation qam constellation by a continuous uniform distribution we also derive the modified cramer rao bound crb for noise variance estimation then the optimal moment pair is found from minimizing the mean squared error mse of the signal to noise ratio snr the method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed

dynamics of polynomial mappings of c 2 we study the dynamics of polynomial self mappings f of c 2 we construct for a large class of mappings an invariant measure which is mixing and of maximal entropy h f max log d t f log 1 f where d t f is the topological degree of f and 1 f its first dynamical degree to achieve this we look at the meromorphic extensions of f to smooth minimal compactifications of c 2 when a good compactification is found we construct an f invariant green current t which contains many dynamical informations when d t f 1 f 1 the measure is obtained as p dd c vt where v is a partial green function defined on the support of t when 1 t t where t is a globally defined f invariant current

polynomial diffeomorphisms of c 2 viii quasi expansion we introduce the notion of quasi expansion in the context of polynomial diffeomorphisms of c 2 like hyperbolic diffeomorphisms quasi expanding maps have uniformly large multipliers at saddle points on the other hand unlike the hyperbolic case quasi expanding maps can have tangencies between stable and unstable manifolds we characterize quasi expansion in a number of ways and develop some of the structure they possess quasi expansion was motivated by the study of real polynomial diffeomorphisms of maximal entropy and our study of maximal entropy diffeomorphisms relies on the results of this paper

polynomial diffeomorphisms of ii stable manifolds and recurrence f x y y y ax c the diffeomorphisms in this class have complicated dynamics in particular they have periodic points of infinitely many periods and positive topological entropy see fm s we can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism define deg f to be the maximum of the degrees of the coordinate functions this quantity is not a conjugacy invariant of f hence not a dynamical invariant we can construct a conjugacy invariant which we call the dynamical degree as follows

on the dynamics of nondegenerate polynomial endomorphisms of c2 abstract we generalize the brolin lyubich theorem for nondegenerate polynomial endomorphisms of c 2 we prove for a nondegenerate polynomial endomorphism p with the hyperbolic restriction to the line at infinity that its canonical invariant current p is a complex cycle near the line at infinity in the sense of sullivan invent math 36 1976 225 255

dynamical compactifications of c 2 we find good dynamical compactifications for arbitrary polynomial mappings of c 2 and use them to show that the degree growth sequence satisfies a linear integral recursion formula for maps of low topological degree we prove that the green function is well behaved for maps of maximum topological degree we give normal forms

l alternative de tits pour aut c2 resume via une action de aut c 2 sur un arbre nous classifions les sous groupes de aut c 2 en particulier nous montrons que l alternative de tits est verifiee d autre part nous obtenons une reformulation de la notion de fonction de green pour un automorphisme de type henon copyright 2001 academic press letting aut c 2 act on a tree we classify the subgroups of aut c 2 and show that the tits alternative is true further we get another formulation for the notion of a green function of an henon type automorphism

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

dynamics of transcendental henon maps the dynamics of transcendental functions in the complex plane has received a significant amount of attention in particular much is known about the description of fatou components besides the types of periodic fatou components that can occur for polynomials there also exist so called baker domains periodic components where all orbits converge to infinity as well as wandering domains in trying to find analogues of these one dimensional results it is not clear which higher dimensional transcendental maps to consider in this paper we find inspiration from the extensive work on the dynamics of complex henon maps we introduce the family of transcendental henon maps and study their dynamics emphasizing the description of fatou components we prove that the classification of the recurrent invariant fatou components is similar to that of polynomial henon maps and we give examples of baker domains and wandering domains

julia set describes quantum tunnelling in the presence of chaos we find that characteristics of quantum tunnelling in the presence of chaos can be regarded as a manifestation of the julia set of the complex dynamical system several numerical pieces of evidence for the standard map together with a rigorous statement for the henon map are presented demonstrating that the complex classical paths which contribute to the semiclassical propagator are dense in the julia set chaotic tunnelling can thus be characterized by the transitivity of the dynamics and high density of the trajectories on the julia set

henon like mappings in c we study the dynamics of a class of nonalgebraic holomorphic diffeomorphisms topo logical analogues in the unit bidisk of complex h6non mappings in c2 in particular a dynamical degree is defined which is related to topological entropy and we construct stable unstable invariant currents and prove there is a unique mixing measure of maximal entropy with product structure 1 introduction one of the most famous 2 dimensional dynamical systems is smale s horseshoe it is a basic example of a simple map with complicated dynamics and has served as a guideline for the whole modern development of discrete time dynamical systems a very natural problem in this context is to understand the dynamical phenomena occuring when uniform hyperbolicity of the horseshoe degenerates this was a motivation for the study of the so called henon map

hyperbolic polynomial diffeomorphisms of c2 i a non planar map abstract in this paper we develop a general framework for verifying hyperbolicity of holomorphic dynamical systems in c 2 our framework in particular enables us to construct the first example of a hyperbolic henon map of c 2 which is non planar i e which is not topologically conjugate on its julia set to a small perturbation of any expanding polynomial in one variable the key ideas in its proof are the poincare box which is a building block to apply our criterion for hyperbolicity an operation called fusion to merge two polynomials in one variable to obtain essentially two dimensional dynamics and rigorous computation by using interval arithmetic some conjectures and problems are also presented

snr estimation for multilevel constellations using higher order moments the performance of existing moments based non data aided nda estimators of signal to noise ratio snr in digital communication systems substantially degrades with multilevel constellations we propose a novel moments based approach that is amenable to practical implementation and significantly improves on previous estimators of this class this approach is based on a linear combination of ratios of certain even order moments which allow the derivation of nda snr estimators without requiring memory costly lookup tables the weights of the linear combination can be tuned according to the constellation and the snr operation range as particular case we develop an eighth order statistics eos based estimator showing in detail the statistical analysis that leads to the weight optimization procedure the eos based estimators yield improved performance for multilevel constellations especially for those with two and three amplitude levels monte carlo simulations validate the new approach in a wide snr range

an envelope based feature for nda snr estimation signal to noise ratio snr estimation is essential in many communication systems moment based snr estimators are a type of envelope based estimator the performance of moment based estimators are known to decrease with increasing snr for nonconstant modulus signals in this paper an envelopebased feature is proposed to overcome the challenges posed by nonconstant modulus signals the feature extraction and estimation processes are presented and the results are shown the newly proposed estimator performs better than classical moment based estimators for modulations such as quadrature amplitude modulations qam and amplitude and phase shift keying apsk modulations

stability and bifurcations for dissipative polynomial automorphisms of mathbb c 2 we study stability and bifurcations in holomorphic families of polynomial automorphisms of mathbb c 2 we say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there we first show that this defines a meaningful notion of stability which parallels in many ways the classical notion of j stability in one dimensional dynamics define the bifurcation locus to be the complement of the weak stability locus in the second part of the paper we prove that under an assumption of moderate dissipativity the parameters displaying homoclinic tangencies are dense in the bifurcation locus this confirms one of palis conjectures in the complex setting the proof relies on the formalism of semi parabolic bifurcation and the construction of critical points in semi parabolic basins which makes use of the classical denjoy carleman ahlfors and wiman theorems

fine topology silov boundary and ddc n on considere la topologie fine des fonctions plurisousharmoniques on etablit des theoremes de convergence on etudie les definitions de dd c n l operateur dd c n converge pour des limites monotones des fonctions plurisousharmoniques bornees

dynamics of regular polynomial endomorphisms of c k a regular polynomial self mapping of complex euclidean space has a continuous extension to the hyperplane at infinity the induced mapping at infinity is used to describe the dynamics of the self mapping in a neighborhood of infinity a theory of external rays is developed to provide the connection between the behavior at infinity and the behavior on the finite plane

on loops in the hyperbolic locus of the complex henon map and their monodromies abstract we prove john hubbard s conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex henon map in fact we show that there exist several non trivial loops in the locus which generate infinitely many mutually different monodromies furthermore we prove that the dynamics of the real henon map is completely determined by the monodromy of the complex henon map providing the parameter of the map is contained in the hyperbolic horseshoe locus

the julia set of henon maps in this paper we investigate the support of the unique measure of maximal entropy of complex henon maps j the main question is whether this set is the same as the analogue of the julia set j

data aided and non data aided maximum likelihood snr estimators for cpm data aided da and non data aided nda maximum likelihood ml estimators for the snr of cpm in the presence of phase and frequency offset are derived and analyzed cramer rao bounds for both are obtained and compared to the simulated performance of these estimators for a full response example cpsfk and a partial response example gmsk analysis and simulations show that the performance of the da ml estimator suffers from an unremovable bias caused by uncompensated frequency offset due to frequency offset estimation errors as a consequence the estimator error variance of the da ml estimator is not able to achieve its lower bound in contrast the estimator error variance of the nda ml estimator is capable of achieving its lower bound although the lower bound for nda ml estimator is higher than the lower bound for the da ml estimator this is because the nda ml estimator is not burdened with the requirement of relying on estimates of nuisance parameters the nda estimator only achieves its lower bound when the observation length or true snr are sufficiently large

topological entropy on saddle sets in p2 we consider hyperbolic sets of saddle type for holomorphic mappings in p our main result relates topological entropy on such sets to a normal families condition on local unstable manifolds

further remarks on rigidity of henon maps abstract for a henon map h in c 2 we characterize the polynomial automorphisms of c 2 which keep any fixed level set of the green function of h completely invariant the interior of any non zero sublevel set of the green function of a henon map turns out to be a short c 2 and as a consequence of our characterization it follows that there exists no polynomial automorphism apart from possibly the affine automorphisms which acts as an automorphism on any of these short c 2 s further we prove that if any two level sets of the green functions of a pair of henon maps coincide then they almost commute

snr estimation for nonconstant modulus constellations we propose a new technique to estimate the signal to noise ratio snr over the flat fading channel this is a nondata aided envelope based estimator that can be applied to nonconstant modulus constellations which is a feature not found in existing approaches we also analyze the performance of our estimators for both phase shift keying psk and non psk constellations by deriving their asymptotic variances and comparing with the crame spl acute r rao bounds crbs moreover we discuss how the snr estimates can be used to approximate the bit error rate ber and how the accuracy of the snr estimate is related to that of the ber estimate which justifies the necessity for the accurate estimation of snr the analytical performance is shown for both psk and non psk constellations such as 8 quadrature amplitude modulation qam and 16 qam monte carlo simulation results corroborate our analysis

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

a nondata aided snr estimation technique for multilevel modulations exploiting signal cyclostationarity signal to noise ratio snr estimators of linear modulation schemes usually operate at one sample per symbol at the matched filter output in this paper we propose a new method for estimating the snr in the complex additive white gaussian noise awgn channel that operates directly on the oversampled cyclostationary signal at the matched filter input exploiting cyclostationarity proves to be advantageous due to the fact that a signal free euclidean noise subspace can be identified such that only second order moments of the received waveform need to be computed the proposed method is nondata aided nda as well as constellation and phase independent and only requires prior timing synchronization to fully exploit the cyclostationarity property the estimator can also be applied to nonconstant modulus constellations without requiring any tuning which is a feature not found in existing approaches implementation aspects and simpler suboptimal solutions are also provided

post critical set and non existence of preserved meromorphic 2 forms we present a family of birational transformations in cp2 depending on two or three parameters which do not generically preserve meromorphic 2 forms with the introduction of the orbit of the critical set vanishing condition of the jacobian also called the post critical set we get some new structures some non analytic 2 form which reduce to meromorphic 2 forms for particular subvarieties in the parameter space on these subvarieties the iterates of the critical set have a polynomial growth in the degrees of the parameters while one has an exponential growth out of these subspaces the analysis of our birational transformation in cp2 is first carried out using the diller favre criterion in order to find the complexity reduction of the mapping the integrable cases are found the identification between the complexity growth and the topological entropy is once again verified we perform plots of the post critical set as well as calculations of lyapunov exponents for many orbits confirming that generically no meromorphic 2 form can be preserved for this mapping these birational transformations in cp2 which generically do not preserve any meromorphic 2 form are extremely similar to other birational transformations we previously studied which do preserve meromorphic 2 forms we note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned but drastically different results as far as a more probabilistic approach of dynamical systems is concerned lyapunov exponents with these examples we see that the existence of a preserved meromorphic 2 form explains most of the numerical discrepancies between the topological and probabilistic approaches of dynamical systems

on measures of maximal and full dimension for polynomial automorphisms of ℂ for a hyperbolic polynomial automorphism of c 2 we show the existence of a measure of maximal dimension and identify the conditions under which a measure of full dimension exists

maximum likelihood snr estimation of linearly modulated signals over time varying flat fading simo channels in this paper we tackle for the first time the problem of maximum likelihood ml estimation of the signal to noise ratio snr parameter over time varying single input multiple output simo channels both the data aided da and the non data aided nda schemes are investigated unlike classical techniques where the channel is assumed to be slowly time varying and therefore considered as constant over the entire observation period we address the more challenging problem of instantaneous i e short term or local snr estimation over fast time varying channels the channel variations are tracked locally using a polynomial in time expansion first we derive in closed form expressions the da ml estimator and its bias the latter is subsequently subtracted in order to obtain a unbiased da estimator whose variance and the corresponding cramer rao lower bound crlb are also derived in closed form due to the extreme nonlinearity of the log likelihood function llf in the nda case we resort to the expectation maximization em technique to iteratively obtain the exact nda ml snr estimates within very few iterations most remarkably the new em based nda estimator is applicable to any linearly modulated signal and provides sufficiently accurate soft estimates i e soft detection for the unknown transmitted symbols therefore hard detection can be easily embedded in the iteration loop in order to improve its performance at low snr levels we show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per antenna snrs as they coincide with the da crlb over a wide range of practical snrs

complex henon maps and discrete groups abstract consider the standard family of complex henon maps h x y p x a y x where p is a quadratic polynomial and a is a complex parameter let u be the set of points that escape to infinity under forward iterations the analytic structure of the escaping set u is well understood from previous work of j hubbard and r oberste vorth as a quotient of c d c by a discrete group of automorphisms isomorphic to z 1 2 z on the other hand the boundary j of u is a complicated fractal object on which the henon map behaves chaotically we show how to extend the group action to s 1 c in order to represent the set j as a quotient of s 1 c by an equivalence relation we analyze this extension for henon maps that are perturbations of hyperbolic polynomials with connected julia set or polynomials with a parabolic fixed point

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

on commuting polynomial automorphisms of mathbb c k k 3 we characterize the polynomial automorphisms of mathbb c 3 which commute with a regular automorphism we use their meromorphic extension to mathbb p 3 and consider their dynamics on the hyperplane at infinity we conjecture the additional hypothesis under which the same characterization is true in all dimensions we give a partial answer to a question of s smale that in our context can be formulated as follows can any polynomial automorphism of mathbb c k be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer i e c f simeq mathbb z

semi parabolic bifurcations in complex dimension two parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena in this paper we consider the bifurcations of a holomorphic diffeomorphism in two complex dimensions with a semi parabolic semiattracting fixed point

automatic classification of single facial images we propose a method for automatically classifying facial images based on labeled elastic graph matching a 2d gabor wavelet representation and linear discriminant analysis results of tests with three image sets are presented for the classification of sex race and expression a visual interpretation of the discriminant vectors is provided

blind signal to noise ratio estimation of real sinusoid in additive noise we consider the problem of estimation of signal to noise ratio snr with a real deterministic sinusoid with unknown frequency phase and amplitude in additive gaussian noise of unknown variance the method of moments a general method to derive estimators based on high order moments is used to derive a blind snr estimator that does not require the knowledge of the instantaneous frequency of the sinusoid through separate estimation of signal and noise power cramer rao lower bounds crlbs are also derived for estimators of signal and noise power and then for snr estimators we show through numerical simulations the statistical performances of the estimators that we compare to the corresponding crlbs and discuss their use in practical applications

polynomial skew products with wandering fatou disks until recently little was known about the existence of wandering fatou components for rational maps in more than one complex variables in 2014 examples of wandering fatou components were constructed in astorg et al 1 for polynomial skew products with an invariant parabolic fiber in 2004 lilov already proved the non existence of wandering fatou components for polynomial skew products in the basin of an invariant super attracting fiber in the current work we investigate in how far his methods carry over to the geometrically attracting case lilov proved a stronger statement namely that the orbit of any horizontal disk in the super attracting basin must eventually intersect a fattened fatou components here we give explicit constructions to show that this stronger result is false in the geometrically attracting case however we also prove that the constructed disks do not give rise to wandering fatou components our construction therefore leaves open the existence of wandering fatou components in the geometrically attracting case showing however that the situation is significantly more complicated than in the super attracting case

a structure theorem for semi parabolic henon maps abstract consider the parameter space p c 2 of complex henon maps h c a x y x 2 c a y a x a 0 which have a semi parabolic fixed point with one eigenvalue e 2 i p q in this paper we provide a complete topological description of the julia set and forward julia set within a family of semi parabolic henon maps i e those henon maps from the curve p which are perturbations of a quadratic polynomial p with a parabolic fixed point of multiplier we prove that there is an open disk of parameters in p for which the semi parabolic henon map has connected julia set j and is structurally stable on j and j the forward julia set j has a nice local description inside a certain bidisk it is a trivial fiber bundle over j p the julia set of the polynomial p with fibers biholomorphic to a disk the julia set j is homeomorphic to the quotient of a solenoid by an equivalence relation and j j the closure of the saddle periodic points

energy and invariant measures for birational surface maps given a birational self map of a compact complex surface it is useful to find an invariant measure that relates the dynamics of the map to its action on cohomology under a very weak hypothesis on the map we show how to construct such a measure the main point in the construction is to make sense of the wedge product of two positive closed 1 1 currents we are able to do this in our case because local potentials for each current have finite energy with respect to the other our methods also suffice to show that the resulting measure is mixing does not charge curves and has nonzero lyapunov exponents

gain control free near efficient phase acquisition for qam constellations this paper introduces a novel not data aided phase offset estimator for quadrature amplitude modulated qam signals contrarily to near efficient existing phase acquisition techniques this estimator does not require a preliminary gain adjustment stage while its accuracy preserves the slope of cramer rao bound for medium high signal to noise ratio snr ranges where it typically outperforms existing blind estimators with significant improvement for dense and cross qam constellations moreover it needs only a very rough estimate of the snr like other gain control free blind phase offset estimators it measures the amount of the cyclic shift by which the four folded phase probability density function pdf is rotated under an unknown phase offset estimation of the phase offset induced cyclic shift is conducted first by measuring the received data phase pdf by a canonical phase histogram procedure then by estimating the phase offset induced cyclic shift through a cyclic cross correlation based procedure between the measured phase histogram and a reference phase pdf evaluated within the zero phase offset hypothesis actually the estimation procedure is presented in a generalized version that considers a tomographic projection of the bidimensional magnitude phase pdf of suitable nonlinear transformations of the received data the tomographic projection performs a magnitude weighing on the pdf and this in turn results in an improved overall estimation accuracy as shown by theoretical analysis and numerical simulations here performed to assess the estimator performance

generalized physical and srb measures for hyperbolic diffeomorphisms in this paper we introduce the notion of generalized physical and srb measures these measures naturally generalize classical physical and srb measures to measures which are supported on invariant sets that are not necessarily attractors we then perform a detailed case study of these measures for hyperbolic henon maps for this class of systems we are able to develop a complete theory about the existence uniqueness finiteness and properties of these natural measures moreover we derive a classification for the existence of a measure of full dimension we also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of as well as the differences to the results for henon maps finally we study the regular dependence of the dimension of the generalized physical srb measure on the diffeomorphism for the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism

cramer rao lower bound and em algorithm for envelope based snr estimation of nonconstant modulus constellations signal to noise ratio snr estimation for linearly modulated signals is addressed in this letter focusing on envelope based estimators which are robust to carrier offsets and phase jitter and on the challenging case of nonconstant modulus constellations for comparison purposes the true cramer rao lower bound is numerically evaluated obtaining an analytical expression in closed form for the asymptotic case of high snr values which quantifies the performance loss with respect to coherent estimation as the maximum likelihood algorithm is too complex for practical implementation an expectation maximization em approach is proposed achieving a good tradeoff between complexity and performance for medium to high snrs finally a hybrid scheme based on em and moments based estimates is suggested which performs close to the theoretical limit over a wide snr range

kupka smale theorem for polynomial automorphisms of ℂ2 and persistence of heteroclinic intersections a map is kupka smale if all periodic points are hyperbolic and the stable and unstable manifolds of any two saddle points are transverse here we prove that kupka smale maps form a residual set of full lebesgue measure in the space mathcal p d of polynomial automorphisms of 2 of fixed dynamical degree d 2 we also prove that a heteroclinic point of two saddle periodic orbits may be continued over almost the entire parameter space for this set of maps this is one of the first persistence theorems proved in holomorphic dynamics in several variables

the equidistribution of small points for strongly regular pairs of polynomial maps in this paper we prove the equidistribution of periodic points of a regular polynomial automorphism f mathbb a n rightarrow mathbb a n defined over a number field k let f be a regular polynomial automorphism defined over a number field k and let v in m k then there exists an f invariant probability measure mu f v on mathrm berk bigl mathbb p n mathbb c v bigr such that the set of periodic points of f is equidistributed with respect to mu f v

facial expression recognition using kernel canonical correlation analysis kcca in this correspondence we address the facial expression recognition problem using kernel canonical correlation analysis kcca following the method proposed by lyons et al and zhang et al we manually locate 34 landmark points from each facial image and then convert these geometric points into a labeled graph lg vector using the gabor wavelet transformation method to represent the facial features on the other hand for each training facial image the semantic ratings describing the basic expressions are combined into a six dimensional semantic expression vector learning the correlation between the lg vector and the semantic expression vector is performed by kcca according to this correlation we estimate the associated semantic expression vector of a given test image and then perform the expression classification according to this estimated semantic expression vector moreover we also propose an improved kcca algorithm to tackle the singularity problem of the gram matrix the experimental results on the japanese female facial expression database and the ekman s pictures of facial affect database illustrate the effectiveness of the proposed method

dynamics of a quadratic map in two complex variables abstract we study the map c 2 c 2 defined by w z z z w2 and the associated collection of sequences zj satisfying the recurrence zj 2 zj 1 z2j iteration of is equivalent to the study of such sequences we analyze growth rates of the sequences positive sequences periodic and asymptotically periodic sequences and establish the existence of doubly infinite homoclinic sequences non zero sequences whose limits as j are 0 we investigate some associated functional equations f x 2 f x 1 f x 2 and l l x l x x2