nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

determining mixed linear nonlinear coupled differential equations from multivariate discrete time series sequences abstract a new method is described for extracting mixed linear nonlinear coupled differential equations from multivariate discrete time series data it is assumed in the present work that the solution of the coupled ordinary differential equations can be represented as a multivariate volterra functional expansion a tractable hierarchy of moment equations is generated by operating on a suitably truncated volterra functional expansion the hierarchy facilitates the calculation of the coefficients of the coupled differential equations in order to demonstrate the method s ability to accurately estimate the coefficients of the governing differential equations it is applied to data derived from the numerical solution of the lorenz equations with additive noise the method is then used to construct a dynamic global mid and high magnetic latitude ionospheric model where nonlinear phenomena such as period doubling and quenching occur it is shown that the estimated inhomogeneous coupled second order differential equation model for the ionospheric fof2 peak plasma density can accurately forecast the future behaviour of a set of ionosonde stations which encompass the earth finally the method is used to forecast the future behaviour of a portfolio of japanese common stock prices the hierarchy method can be used to characterise the observed behaviour of a wide class of coupled linear and mixed linear nonlinear phenomena

computer evaluation of kauffman polynomials by using gauss codes with a skein template algorithm homfly polynomials of knots and links are evaluated on computers by using an algebraic version with gauss codes of the skein template algorithm the computer codes are written with the language c whose structure is particularly suitable to such evaluations jones conway and alexander polynomials may then be readily obtained as special cases

constructing nonautonomous differential equations from experimental time series an approach to constructing model differential equations of harmonically driven systems is proposed it is a modification of the standard global reconstruction technique an algebraic polynomial which coefficients depend on time is used for approximation efficiency and details of the approach are demonstrated by various numerical and natural examples

is the dimension of chaotic attractors invariant under coordinate changes several different dimensionlike quantities which have been suggested as being relevant to the study of chaotic attractors are examined in particular we discuss whether these quantities are invariant under changes of variables that are differentiable except at a finite number of points it is found that some are and some are not it is suggested that the word dimension be reversed only for those quantities have this invariance property

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

building dynamical models from data and prior knowledge the case of the first period doubling bifurcation this paper reviews some aspects of nonlinear model building from data with gray box and without black box prior knowledge the model class is very important because it determines two aspects of the final model namely i the type of nonlinearity that can be accurately approximated and ii the type of prior knowledge that can be taken into account such features are usually in conflict when it comes to choosing the model class the problem of model structure selection is also reviewed it is argued that such a problem is philosophically different depending on the model class and it is suggested that the choice of model class should be performed based on the type of a priori available a procedure is proposed to build polynomial models from data on a poincare section and prior knowledge about the first period doubling bifurcation for which the normal form is also polynomial the final models approximate dynamical data in a least squares sense and by design present the first period doubling bifurcation at a specified value of parameters the procedure is illustrated by means of simulated examples

meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature abstract we give a detailed description of the schwartz kernel of the resolvent of the laplacian on a certain class of complete riemannian manifolds with negative sectional curvature near infinity these manifolds have compactifications as c manifolds with boundary on which the metric is conformai to a c metric up to the boundary with conformal factor 2 where is a defining function for the boundary the modified resolvent r s 2 n 1 defined and analytic in r n is shown to extend to be meromorphic in the whole complex plane when s 2 is equal to the sectional curvature at infinity for hyperbolic spaces obtained as quotients hn 1 where is a discrete group of fractional linear transformations having a geometrically finite fundamental domain without cusps at infinity s is constant we then deduce from the existence of this meromorphic extension of the resolvent the existence of a similar extension for the eisenstein series the basic method used to produce a parametrix for the laplacian is part of a more general construction by g mendoza and the second author but since this is not yet available the present paper has been made essentially self contained

global vector field reconstruction by using a multivariate polynomial l 2 approximation on nets a multivariate polynomial mathit l 2 approximation on nets is designed for global vector field reconstructions of time continuous dynamical systems the technique is tested by investigating standard forms of the r ossler band the lorenz mask and a chaotic attractor produced by a simple model of thermal lens oscillations

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

on the non equivalence of observables in phase space reconstructions from recorded time series in practical problems of phase space reconstruction it is usually the case that the reconstruction is much easier using a particular recorded scalar variable this seems to contradict the general belief that all variables of a dynamical system are equivalent in phase space reconstruction problems this paper will argue that in many cases the choice of a particular scalar time series from which to reconstruct the original dynamics could be critical it is argued that different dynamical variables do not provide the same level of information observability of the underlying dynamics and as a consequence the quality of a global reconstruction critically depends on the recorded variable examples in which the choice of observables is critical are discussed and the level of information contained in a given variable is quantified in the case where the original system is known a clear example of such a situation arises in the r ossler system for which the performance of a global vector field reconstruction technique is investigated using time series of variables x y or z taken one at a time

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

lorentzian einstein metrics with prescribed conformal infinity we prove a local well posedness theorem for the n 1 dimensional einstein equations in lorentzian signature with initial data widetilde g k whose asymptotic geometry at infinity is similar to that anti de sitter ads space and compatible boundary data widehat g prescribed at the time like conformal boundary of space time more precisely we consider an n dimensional asymptotically hyperbolic riemannian manifold m widetilde g such that the conformally rescaled metric x 2 widetilde g with x a boundary defining function extends to the closure overline m of m as a metric of class c n 1 overline m which is also poly homogeneous of class c p mathrm polyhom overline m likewise we assume that the conformally rescaled symmetric 0 2 tensor x 2 k extends to overline m as a tensor field of class c n 1 overline m which is polyhomogeneous of class c p 1 mathrm polyhom overline m we assume that the initial data widetilde g k satisfy the einstein constraint equations and also that the boundary datum is of class c p on partial m times t 0 t 0 and satisfies a set of natural compatibility conditions with the initial data we then prove that there exists an integer r n depending only on the dimension n such that if p geqslant 2q r n with q a positive integer then there is t gt 0 depending only on the norms of the initial and boundary data such that the einstein equations 1 1 has a unique up to a diffeomorphism solution g on t t times m with the above initial and boundary data which is such that x 2 g in c n 1 t t times overline m cap c q mathrm polyhom t t times overline m furthermore if x 2 widetilde g x 2 k are polyhomogeneous of class c infty and widehat g is in c infty t 0 t 0 times partial overline m then x 2 g is in c infty mathrm polyhom t t times overline m

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

discrete time dynamical system under observational uncertainty abstract discrete time dynamical systems under observational uncertainty are studied as a result of the uncertainty points on an orbit are surrounded by uncertainty sets the problem of reconstructing the original orbit given the sequence of uncertainty sets is investigated the key property which makes the reconstruction possible is the sensitivity to initial conditions a general reconstructing algorithm is theoretically analyzed and experimentally tested on several low dimensional systems the technique is extended to coupled one dimensional maps with the goal of eventually developing retrospective techniques for partial differential equations exhibiting spatio temporal chaos provided the coupling strength remains small and the coupling term has bounded first derivatives it is conjectured that for dynamical systems with a positive liapunov exponent the observational uncertainty can be reduced exponentially with the length of the orbit used for reconstruction computer experiments with the coupled logistic map are consistent with this conjecture

classification of strange attractors by integers we show how to characterize a strange attractor by a set of integers these are extracted from the chaotic time series data by first reconstructing the low period orbits and then determining the template or knot holder which supports all periodic orbits embedded in the strange attractor and the strange attractor itself the template is identified by a set of integers which therefore characterize the strange attractor this identification is explicitly demonstrated for the pirogon using a relatively small data set 5000 points

quantifying local predictability in phase space abstract both the classical lyapunov exponents and the quantities from which they are derived the local divergence rates characterize the behavior of initially adjacent trajectories in phase space the exponents are the long term averages of this divergence while the local rates quantify the behavior of nearby trajectories as a function of time and phase space position thus given a transient free initial state the local divergence rates provide estimates of short term predictability along the resultant trajectory we calculate local divergence rates for the chaotic attractor of the three component lorenz model and we investigate both the temporal and phase spatial variations in predictability we show quantitatively that predictability varies considerably with time but that there is phase spatial organization to the variability this underlying structure permits identification of regions in phase space of high and low predictability and in some cases it permits an estimate of predictability to be assigned to the predictability variable itself

observability of multivariate differential embeddings the present paper extends some results recently developed for the analysis of observability in nonlinear dynamical systems the aim of the paper is to address the problem of embedding an attractor using more than one observable a multivariate nonlinear observability matrix is proposed which includes the monovariable nonlinear and linear observability matrices as particular cases using the developed framework and a number of worked examples it is shown that the choice of embedding coordinates is critical moreover in some cases to reconstruct the dynamics using more than one observable could be worse than to reconstruct using a scalar measurement finally using the developed framework it is shown that increasing the embedding dimension observability problems diminish and can even be eliminated this seems to be a physically meaningful interpretation of the takens embedding theorem

construction of phenomenological models from numerical scalar time series abstract the problem of reconstruction of ordinary differential equations from numerical scalar time series is discussed techniques are exemplified for rossler and lorenz chaotic attractors with emphasis on improved algorithms with respect to those previously published the steps which are still required in order to investigate experimental noisy data are discussed

statistical description of chaotic attractors the dimension function a method for the investigation of fractal attractors is developed based on statistical properties of the distributionp n of nearest neighbor distances between points on the attractor a continuous infinity of dimensions called dimension function is defined through the moments ofp n in particular for the case of self similar sets we prove that the dimension function df yields in suitable points capacity information dimension and all other renyi dimensions an algorithm to compute df is derived and applied to several attractors as a consequence an estimate of nonuniformity in dynamical systems can be performed either by direct calculation of the uniformity factor or by comparison among various dimensions finally an analytical study of the distributionp n is carried out in some simple meaningful examples

focusing filters for wide band direction finding a time domain equivalent of the coherent signal subspace transformations cst is established for wideband direction finding in a possible multipath environment using general arrays time domain equivalents of focusing are derived based on the least squared error approach for general transformations and the taylor series expansion approach for closed form transformations the preprocessor is realized by a multichannel digital finite impulse response filter for diagonal transformations the problem reduces to implementing different delays at each sensor which in turn leads to computational simplicity various tapped delay line filters for realizing an arbitrary delay are proposed and compared simulation results reveal that low order filter structures in the time domain achieve similar performance to the frequency domain approach even at detection and resolution thresholds

explicit formula and meromorphic extension of the resolvent for the massive dirac operator in the schwarzschild anti de sitter spacetime we study the resolvent of the massive dirac operator in the schwarzschild anti de sitter space time after separation of variables we use standard one dimensional techniques to obtain an explicit formula we then make use of this formula to extend the resolvent meromorphically across the real axis

boundedness and growth for the massive wave equation on asymptotically anti de sitter black holes abstract we study the global dynamics of free massive scalar fields on general globally stationary asymptotically ads black hole backgrounds with dirichlet neumann or robin boundary conditions imposed on at infinity this class includes the regular kerr ads black holes satisfying the hawking reall bound r 2 a l we establish a suitable criterion for linear stability in the sense of uniform boundedness of and demonstrate how the issue of stability can depend on the boundary condition prescribed in particular in the slowly rotating kerr ads case we obtain the existence of linear scalar hair i e non trivial stationary solutions for suitably chosen robin boundary conditions