Related papers: Directional complexity and entropy for lift mappin…

The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…

In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…

In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set)…

We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…

In this work we study the main dynamical properties of the push-forward map, a transformation in the space of probabilities P(X) induced by a map T: X \to X, X a compact metric space. We also establish a connection between topological…

For a continuous map on a topological graph containing a unique loop S it is possible to define the degree and, for a map of degree 1, rotation numbers. It is known that the set of rotation numbers of points in S is a compact interval and…

We study the Manneville map f(x)=x+x^z (mod 1), with z>1, from a computational point of view, studying the behaviour of the Algorithmic Information Content. In particular, we consider a family of piecewise linear maps that gives examples of…

We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on…

We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…

We introduce a series of discrete mappings, which is considered to be an extension of the Hietarinta-Viallet mapping with one parameter. We obtain the algebraic entropy for this mapping by obtaining the recurrence relation for the degrees…

We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been…

A numerical code is described for constructing Doppler maps from the orbital variation of line profiles of (mass transfering) binaries. It uses an algorithm related to Richardson-Lucy iteration, and is much faster than the standard…

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as…

In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations…

We analyze the behaviour of two quantum dynamical entropies in connection with the classical limit. Using strongly chaotic classical dynamical systems as models (Arnold Cat Maps and Sawtooth Maps), we also propose a discretization procedure…

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the…

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time…