Symbolic dynamics and geodesic flows
Symbolic dynamics and Lyapunov exponents for Lozi maps
Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.
Symplectic rigidity of geodesic flows on two-step nilmanifolds
Synchronization in ensembles of coupled maps with a major element.
Synchronization with error bound of non-identical forced oscillators
Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.
Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map.
Synthesis of chaotic systems
Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale
Soit un difféomorphisme d’une surface possédant deux fers à cheval tels que et aient en un point une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de et est strictement plus grande que 1, les difféomorphismes voisins de tels que et soient stablement tangents au voisinage de forment une partie de densité inférieure strictement positive en .
Teorie deterministického chaosu a některé její aplikace (1. část)
Teorie deterministického chaosu a některé její aplikace (2. část)
The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
The Algebraic Integrability of Geodesic Flow on S0(4).
The Art and Science of Symmetric Design
The attractors of the common differential operator are determined by hyperbolic and lacunary functions.
The average length of a trajectory in a certain billiard in a flat two-torus.
The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations
In this paper piecewise monotonic maps are considered. Let be a finite union of open intervals, and consider the set of all points whose orbits omit . The influence of small perturbations of the endpoints of the intervals in on the dynamical system is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed by arbitrary...
The Bernoulli shift as a basic chaotic dynamical system
We give a brief introduction to the Bernoulli shift map as a basic chaotic dynamical system. We give several examples where the iterates of a~mapping can be understood using the Bernoulli shift. Namely, the iteration of real interval maps and iteration of quadratic functions in the complex plain.
The bitransitive continuous maps of the interval are conjugate to maps extremely chaotic a. e.
The interior of zero entropy diffeomorphisms.
The hypothesis in Pesin theory