Ergodic properties and KMS conditions on -symbolic dynamical systems.
Ergodic theory approach to chaos: Remarks and computational aspects
We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a...
Ergodic theory of interval exchange maps.
A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichmüller flows, starting from the basic definitions and culminating with the proof that almost every interval exchange map is uniquely ergodic. Great emphasis is put on examples and geometric interpretations of the main ideas.
Ergodicity of Anosov Actions.
Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces.
Erratum to "Multifractal spectra of Birkhoff averages for a piecewise monotone interval map" (Fund. Math. 208 (2010), 95-121)
Essential dynamics for Lorenz maps on the real line and the lexicographical world
Estimation de l'entropie des systèmes lagrangiens sans points conjugués
Étude d’une transformation non uniformément hyperbolique de l’intervalle
Nous étudions un exemple de transformation non uniformément hyperbolique de l’intervalle . Des exemples analogues ont été étudiés par de nombreux auteurs. Notre méthode utilise une théorie spectrale, pour une classe d’opérateurs vérifiant des conditions faibles de Doeblin-Fortet, introduite dans [1]. Elle nous permet, en particulier, de donner une estimation de la vitesse de décroissance des corrélations pour des fonctions non höldériennes.
Eventually periodic points of infra-nil endomorphisms.
Exactness of expanding mappings
Exactness of skew products with expanding fibre maps
We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.
Examples of Expanding Endomorphisms on Exotic Tori.
Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation
We prove that for every ϵ > 0 there exists a minimal diffeomorphism f: ² → ² of class and semiconjugate to an ergodic translation with the following properties: zero entropy, sensitivity to initial conditions, and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé’s example of a derived-from-Anosov diffeomorphism on ³.
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Existence of eigenvalues for (uaa) Markov maps.
Existence of non-uniform cocycles on uniquely ergodic systems
Existence of Periodic Points of Maps of S1.
Existence of pullback attractors for the coupled suspension bridge equations.
Existence of unique SRB-measures is typical for real unicritical polynomial families