synchronization time in a hyperbolic dynamical system with long range interactions abstract we show that the threshold of complete synchronization in a lattice of coupled non smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace we examine carefully the synchronization time and show that an inadequate observation of the system evolution leads to wrong results we present both careful numerical experiments and a rigorous mathematical explanation confirming this fact allowing for a generalization involving hyperbolic coupled map lattices

normal forms for periodic systems the theory of normal forms for autonomous differential equations based on the lie bracket has proved to be an important technique in determining the behaviour of solutions of nonlinear differential equations near a stationary solution it has been widely used in the bifurcation theory for autonomous ordinary differential equations see e g 1 3 6 9 11 i in its simplest form the theory applies to an equation of the form

an approach to investigate the instability of the multiple degree of freedom parametric dynamic systems a new analytical approach to the investigation of the regions of instability of multiple degree of freedom parametric dynamic systems is presented upon assuming a solution as a product of a characteristic component and a vector which has a periodic component expanding this vector into a fourier series and substituting it into the governing equations of motion a system of homogeneous algebraic equations can be obtained by the harmonic balance method then the problem of the stability of the non trivial solutions results in an eigenvalue problem of a non symmetricmatrix numerical results are presented for an undamped and damped mathieu equation whose stability has been investigated by various methods of solution the method has been applied to multiple degree of freedom systems such as lateral bending torsional vibration of a thin beam under parametric excitation and the parametric instability of a column under periodically varying axial loads

structure of intermediate wakimoto modules abstract we show that our construction of boson type realizations of affine sl n 1 in terms of intermediate wakimoto modules gives representations that are generically isomorphic to certain verma type modules we then use this identification to obtain information about the submodule structure of intermediate wakimoto modules

on the representation of operators in bases of compactly supported wavelets this paper describes exact and explicit representations of the differential operators d n dx n n 1 2 cdots in orthonormal bases of compactly supported wavelets as well as the representations of the hilbert transform and fractional derivatives the method of computing these representations is directly applicable to multidimensional convolution operators also sparse representations of shift operators in orthonormal bases of compactly supported wavelets are discussed and a fast algorithm requiring o n log n operations for computing the wavelet coefficients of all n circulant shifts of a vector of the length n 2 n is constructed as an example of an application of this algorithm it is shown that the storage requirements of the fast algorithm for applying the standard form of a pseudodifferential operator to a vector see g beylkin r r coifman and v rokhlin comm pure appl math 44 1991 pp 141 183 may be reduced from o n to o log 2 n significant entries

chaos and diffusion in deterministic cellular automata abstract it is shown that some of the deterministic one dimensional cellular automata studied recently by wolfram exhibit a kind of spontaneous symmetry breaking the associated kinks bloch walls perform annihilating diffusive walks for infinite lattices and large times in addition close analogies between these automata and strange attractors are exhibited by mapping the automata onto dynamical systems defined by iterations of the unit square

a generalized bolotin s method for stability limit determination of parametrically excited systems abstract a boundary tracing method is presented for the construction of stability charts for non canonical parametrically excited systems the method is an extension so as to cover the combination resonances of the well known bolotin s method and reduces the boundary tracing problems into an eigenvalue analysis problem of some special matrices

a reduction theorem for highest weight modules over toroidal lie algebras let open image in new window be a toroidal lie algebra corresponding to a semisimple lie algebra open image in new window we describe all borel subalgebras of open image in new window which contain the cartan subalgebra open image in new window where open image in new window is a fixed cartan subalgebra of open image in new window we show that each such borel subalgebra open image in new window determines a parabolic decomposition open image in new window where open image in new window is a proper toroidal subalgebra of open image in new window and open image in new window our first main result is that for any weight which does not vanish on open image in new window an arbitrary subquotient of the verma module open image in new window is induced from its open image in new window submodule of open image in new window invariant vectors this reduces the study of subquotients of open image in new window to the study of subquotients of verma modules over open image in new window we then introduce categories open image in new window and open image in new window and their respective blocks open image in new window and open image in new window corresponding to a central charge which is nonzero on open image in new window our second main result is that the functors of induction and open image in new window invariants are mutually inverse equivalences of the category open image in new window and the full subcategory of open image in new window whose objects are generated by their open image in new window invariants

integrable representations for generalized virasoro toroidal lie algebras abstract in this paper we give the structure of irreducible integrable modules of generalized virasoro toroidal lie algebras with finite dimensional weight spaces and non zero central charge

globally coupled maps phase transitions and synchronization abstract bifurcations in a system of coupled maps are investigated using symbolic dynamics it is shown that for coupled shift maps the well known space time mixing attractor becomes unstable at a critical coupling strength in favour of a synchronized state for coupled non hyperbolic maps analytical and numerical evidence is given that arbitrary small coupling changes the dynamical behaviour the anomalous dependence of fluctuations on the system size is attributed to these bifurcations

stability analysis of periodic systems by truncated point mappings an approach is presented deriving analytical stability and bifurcation conditions for systems with periodically varying coefficients the method is based on apoint mapping period to period mapping representation of the system s dynamics an algorithm is employed to obtain an analytical expression for the point mapping and its dependence on the system s parameters the algorithm is devised to derive the coefficients of a multinominal expansion of the point mapping up to an arbitrary order in terms of the state variables and of the parameters analytical stability and bifurcation condition are then formulated and expressed as functional relations between the parameters to demonstrate the application of the method the parametric stability of mathieu s equation and of a two degree of freedom system are investigated the results obtained by the proposed approach are compared to those obtained by perturbation analysis and by direct integration which we considered to the exact solution it is shown that unlike perturbation analysis the proposed method provides very accurate solution even forlarge valuesof the parameters if an expansion of the point mapping in terms of a small parameter is performed the method is equivalent to perturbation analysis moreover it is demonstrated that the method can be easily applied to multiple degree of freedom systems using the same framework this feature is an important advantage since most of the existing analysis methods apply mainly to single degree of freedom systems and their extension to higher dimensions is difficult and computationally cumbersome

disturbance propagation in chaotic extended systems with long range coupling propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long range couplings decaying as a power of the distance the initial perturbation propagates exponentially fast along the lattice with a rate given by the ratio of the maximal lyapunov exponent and the power of the coupling a complementary description in terms of a suitable comoving lyapunov exponent is also given

analysis of non linear dynamical systems by the normal form theory abstract a method is proposed for calculating the periodic solutions of non linear mechanical systems with analytical non linearities the jordan normalization procedure for the case of non linear autonomous systems is described and generalized to dampened harmonically excited oscillators non linear modes for hamiltonian systems are introduced normal forms simplify the analysis of bifurcation it is shown how to extend the modal synthesis procedure the proposed non linear modes obtained from free vibrations are used to construct a superposition technique to describe the forced response of harmonically excited systems these results are tested for one and two degrees of freedom systems with cubic non linearities the results are compared with expressions obtained by classical analytical methods averaging or multiple scales methods or runge kutta numerical methods

structure of some categories of representations of infinite dimensional lie algebras the highest weight representations of a finite dimensional complex semisimple lie algebra 9 have been studied extensively and a number of interesting results have been obtained in the last few years an extensive bibliography is given in 7 in 2 3 a category cy of representations of g was introduced which turns out to be the proper setting for considering various questions regarding highest weight representations the aim of this paper is to extend the study of this notion to a kac moody algebra or more generally to a contragredient lie algebra g a corresponding to a square matrix a over c the study of such algebras was begun independently in 8 14 and subsequently a number of interesting results were proved these results show that many important properties from the finite dimensional setup i e from the context of 9 can be proved in the general setup involving g a in particular the notion of category was extended in 9 to the case of kac moody algebras and used in the proof of combinatorial identities

synchronization and partial synchronization of linear maps abstract we study synchronization of low dimensional d 2 3 4 chaotic piecewise linear maps that are coupled bidirectionally for bernoulli maps we find lyapunov exponents and locate the synchronization transition which numerically is found to be discontinuous despite continuously vanishing lyapunov exponent s for tent maps a limit of stability of the synchronized state is used to locate the synchronization transition that numerically is found to be continuous for nonidentical tent maps at the partial synchronization transition the probability distribution of the synchronization error is shown to develop highly singular behavior we suggest that for nonidentical bernoulli maps and perhaps some other discontinuous maps partial synchronization is merely a smooth crossover rather than a well defined transition more subtle analysis in the d 4 case locates the point where the synchronized state becomes stable in some cases however a riddled basin attractor appears and synchronized and chaotic behaviors coexist

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

borel subalgebras and categories of highest weight modules for toroidal lie algebras abstract in this article we begin an investigation of the conjugacy classes of borel subalgebras together with verma modules induced from standard borel subalgebras of a toroidal lie algebra t in two variables we define for each highest weight a category o of representations of t that contain these verma modules and show that when a certain central element acts nontrivially this category is equivalent to the category o m for an extension of a suitable affine kac moody algebra m t from this equivalence we obtain a bgg type resolution and bgg duality theorem in the setting of o

nonlinearly driven transverse synchronization in coupled chaotic systems synchronization transitions are investigated in coupled chaotic maps depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur when only two maps are considered we always find that the critical coupling el for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse lyapunov exponent t however major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state as a representative example of extended systems a one dimensional lattice of chaotic maps with power law coupling is considered in this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition for strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above el notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant therefore the transition takes place at a coupling enl definitely larger than el and its origin is intrinsically nonlinear the linearly driven transitions are continuous and can be described in terms of mean field results for non equilibrium phase transitions with long range interactions while the transitions dominated by nonlinear mechanisms appear to be discontinuous

predictability in spatially extended systems the predictability problem is discussed in turbulent fluids and in spatially extended systems we perform a numerical analysis of the spatial propagation of a small perturbation initially localized at a point of a one dimensional lattice of coupled maps where the interactions can be either local or non local in space in both cases the nonlinear terms in the dynamics of the perturbation cannot be neglected and the predictability problem cannot be reduced to the linearized evolution equations only for non local interactions is the predictability time proportional to the inverse lyapunov exponent lambda as in dynamical systems with a few degrees of freedom for local interactions it is proportional to the size of the system and is practically independent of the chaoticity degree lambda

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

correlations and spectra of an intermittent chaos near its onset point a one parameter family of piecewise linear discontinuous maps which bifurcates from a periodic state of periodm m 2 3 to an intermittent chaos is studied as a new model for the onset of turbulence via intermittency the onset of chaos of this model is due to the excitation of an infinite number of unstable periodic orbits and hence differs from pomeau manneville s mechanism which is a collapse of a pair of stable and unstable periodic orbits the invariant density the time correlation function and the power spectrum are analytically calculated for an infinite sequence of values of the bifurcation parameter which accumulate to the onset point c from the chaos side c 0 the power spectrum near 0 is found to consist of a large number of lorentzian lines with two dominant peaks the highest peak lies around frequency 2 m with the power law envelope l 2 m 4 the second highest peak lies around o 0 with the envelope l 2 the width of each line decreases as and the separation between lines decreases as lg3 1 it is also shown that the liapunov exponent takes the form m and the mean lifetime of the periodic state in the intermittent chaos is given bym 1 ln 1 1

central extensions of current groups in this paper we study central extensions of the identity component g of the lie group c m k of smooth maps from a compact manifold m into a lie group k which might be infinite dimensional we restrict our attention to lie algebra cocycles of the form d where y is a symmetric invariant bilinear map on the lie algebra of k and the values of lie in 1 m y dc m y for such cocycles we show that a corresponding central lie group extension exists if and only if this is the case for m 1 if k is finite dimensional semisimple this implies the existence of a universal central lie group extension of g the groups diff m and c m k act naturally on g by automorphisms we also show that these smooth actions can be lifted to smooth actions on the central extension if it also is a central extension of the universal covering group g of g

robust space time intermittency and 1 f noise abstract we investigate a type of intermittency that occurs in space as well as time studying a one dimensional lattice of coupled quadratic maps this system naturally forms spatial domains motion of the domain walls causes spatially localized changes from chaotic to almost periodic behavior the almost periodic phases have eigenvalues quite close to one resulting in long lived laminar bursts with a 1 f low frequency spectrum this behavior has aspects of both crutchfield and pomeau manneville intermittency unlike pomeau manneville however the behavior that we observe here is quite robust under changes of parameters

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

synchronization threshold in coupled logistic map lattices abstract we consider regular lattices of coupled chaotic maps whose local dynamics is ruled by the logistic map x 4 x 1 x a usual paradigm of chaotic systems through finite time exponents we scrutinize the lattice dynamics in the vicinity of the threshold of complete synchronization we connect dynamical features such as relaxation to the coherent state and intermittency with the statistics of finite time exponents focusing on the implications of the particular statistics related to the logistic map although numerical examples are given for lattice couplings decaying with distance as a power law our results are expected to be valid for a wider class of schemes coupling logistic maps

a cell dynamical system model of chemical turbulence a cellular automaton like caricature of chemical turbulence on an infinite one dimensional lattice is studied the model exhibits apparently turbulent space time patterns to make this statement precise the following problems or points are discussed 1 the infinite system size limit of such cell dynamical systems and its observability is defined 2 it is proved that the invariant state in the large system size limit of the turbulent phase exhibits spatial patterns governed by a gibbs random field 3 potential characteristics of turbulent space time patterns are critically surveyed and a working definition of weak turbulence is proposed 4 it is proved that the invariant state of the turbulent phase is actually weak turbulent furthermore we conjecture that the turbulent phase of our model is an example of a k system that is not bernoulli

from multiplicative noise to directed percolation in wetting transitions a simple one dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated upon varying a control parameter the critical behavior observed along the transition line changes from a directed percolation type to a multiplicative noise type numerical simulations allow for a quantitative study of the multicritical point separating the two regions mean field arguments and the mapping on yet a simpler model provide some further insight on the overall scenario

analysis of critical and post critical behaviour of non linear dynamical systems by the normal form method part i normalization formulae abstract a method based on normal form theory is presented to study the dynamical behaviour of a system in the neighbourhood of a nearly critical equilibrium state associated with a bifurcation condition explicit formulae for the normalization procedure are derived these formulae can be numerically programmed avoiding usual complicated algebraic calculations and making the method effectively applicable for n dimensional systems rather general bifurcations can be included e g non linear flutter hopf bifurcation divergence and internal resonance

the computation of wavelet galerkin approximation on a bounded interval this paper describes exact evaluations of various finite integrals whose integrands involve products of daubechies compactly supported wavelets and their derivatives and or integrals these finite integrals play an essential role in the wavelet galerkin approximation of differential or integral equations on a bounded interval

φ imaginary verma modules and their generalizations for the toroidal lie algebras in this paper we first construct a class of weight modules called imaginary verma modules for the toroidal lie algebras then a criterion for the irreducibility of the imaginary verma modules is obtained and the irreducible quotients for the reducible ones are studied furthermore we construct a more general class of n graded modules for the toroidal lie algebras and we discuss their irreducibility this class of modules includes the imaginary verma modules as special examples

a wavelet galerkin procedure to investigate time periodic systems transient vibration and stability analysis abstract a wavelet galerkin procedure is introduced in order to obtain transient and periodic solutions of multi degree of freedom d o f s dynamical systems with time periodic coefficients numerical comparisons achieved with a runge kutta method emphasize that the wavelet based procedure is reliable even in the case of problems involving both smooth or non smooth parametric excitations and a relatively large number of degrees of freedom the procedure is then applied to study the vibrations of some theoretical parametrically excited systems since problems of stability analysis of non linear systems are often reduced after linearization to problems involving linear differential systems with time varying coefficients the method is shown to be effective for the computation of the floquet exponents that characterize stable unstable parameters areas and consequently allows estimators for stability instability levels to be provided stability diagrams of some theoretical examples including a single degree of freedom mathieu oscillator and a two degree of freedom parametrically excited system illustrate the relevance of the method finally future studies are outlined for the extension of the wavelet method to the non linear case

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

relationship between directed percolation and the synchronization transition in spatially extended systems we study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model an analytic argument is put forward showing that in the limit of discontinuous processes the transition belongs to the directed percolation dp universality class the analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold we find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena as a result of this analysis we conclude that the synchronization transition belongs to the dp class also in continuous models the conclusions are supported by numerical checks on coupled map lattices too

linear and nonlinear information flow in spatially extended systems infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated the information transport in these systems can be characterized in terms of the propagation velocity of perturbations vp a linear stability analysis is sufficient to capture all the relevant aspects associated to propagation of infinitesimal disturbances in particular this analysis gives the propagation velocity vl of infinitesimal errors if linear mechanisms prevail on the nonlinear ones vp vl on the contrary if nonlinear effects are predominant finite amplitude disturbances can eventually propagate faster than infinitesimal ones i e vp vl the finite size lyapunov exponent can be successfully employed to discriminate the linear or nonlinear origin of information flow a generalization of the finite size lyapunov exponent to a comoving reference frame allows us to state a marginal stability criterion able to provide vp both in the linear and in the nonlinear case strong analogies are found between information spreading and propagation of fronts connecting steady states in reaction diffusion systems the analysis of the common characteristics of these two phenomena leads to a better understanding of the role played by linear and nonlinear mechanisms for the flow of information in spatially extended systems

an efficient computational scheme for the analysis of periodic systems abstract in this paper a new efficient numerical scheme for the stability analysis of linear systems with periodic parameters is suggested the approach is based on the idea that the state vector and the periodic matrix of the system can be expanded in terms of chebyshev polynomials over the principal period such an expansion reduces the original problem to a set of linear algebraic equations from which the solution in the interval of one period can be obtained furthermore the technique is combined with floquet theory to yield the transition matrix at the end of one period and provide the stability conditions via an eigen analysis procedure two formulations are presented the first formulation is suitable for a set of equations written in state space form while the second can be applied directly to a set of second order equations the application is demonstrated through practical illustrative examples including the parametric excitation problem of a fixed fixed column the numerical results thus obtained are compared with those obtained from dverk a runge kutta code available in the imsl library an error bound analysis is also included it is concluded that the suggested schemes not only provide accurate results but are also computationally very efficient in particular the second formulation is found to be several times faster than the standard runge kutta type codes

forced vibrations of a turbine blade undergoing regularized unilateral contact conditions through the wavelet balance method summary the method of weighted residuals can efficiently enforce time periodic solutions of flexible structures experiencing unilateral contact the harmonic balance method hbm based on fourier expansion of the sought solution is a common formulation although wavelet bases that can sparsely define nonsmooth solutions may be superior this hypothesis is investigated using a full three dimensional blade with unilateral contact conditions on a set of nc discrete contact points located at its tip the unilateral contact conditions are first regularized and a distributional formulation in time is introduced allowing l2 s1 n trial functions to properly approximate in the time domain the solution to the governing equations the mixed wavelet petrov galerkin solutions are found to yield consistent or better results than hbm with higher convergence rates and seemingly more accurate contact force prediction copyright 2014 john wiley sons ltd

transition to stochastic synchronization in spatially extended systems spatially extended dynamical systems namely coupled map lattices driven by additive spatio temporal noise are shown to exhibit stochastic synchronization in analogy with low dimensional systems synchronization can be achieved only if the maximum lyapunov exponent becomes negative for sufficiently large noise amplitude moreover noise can suppress also the nonlinear mechanism of information propagation which may be present in the spatially extended system an example of phase transition is observed when both the linear and the nonlinear mechanisms of information production disappear at the same critical value of the noise amplitude the corresponding critical properties cannot be estimated numerically with great accuracy but some general argument suggests that they could be ascribed to the kardar parisi zhang universality class conversely when the nonlinear mechanism prevails on the linear one another type of phase transition to stochastic synchronization occurs this one is shown to belong to the universality class of directed percolation

emergence of chaotic behaviour in linearly stable systems strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of lyapunov exponents this regime denoted as stable chaos has been so far mainly characterized by means of numerical studies in this paper we investigate the mechanisms that are at the basis of this form of unpredictable evolution generated by a nonlinear information flow through the boundaries in order to clarify how linear stability can coexist with nonlinear instability we construct a suitable stochastic model in the absence of spatial coupling the model does not reveal the existence of any self sustained chaotic phase nevertheless already this simple regime reveals peculiar differences between the behaviour of finite size and that of infinitesimal perturbations a mean field analysis of the spatially extended case provides a semi quantitative description of the onset of irregular behaviour possible relations with directed percolation as a synchronization transition are also briefly discussed

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

characters of irreducible representations of the virasoro algebra on obtient les caracteres des modules irreductibles non integrables de plus haut poids l h 0 on determine les caracteres des familles l t 25 et l t 26 duales de l h 1 et de l h 0

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed