We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in , n ≥ 1, is a σ-limit set for some continuous map.
We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.
Dans cet article, on montre que, dans le groupe des difféomorphismes isotopes à l’identité d’une variété compacte , tout élément récurrent est de distorsion. Pour ce faire, on généralise une méthode de démonstration utilisée par Avila pour le cas de . La méthode nous permet de retrouver un résultat de Calegari et Freedman selon lequel tout homéomorphisme de la sphère isotope à l’identité est un élément de distorsion.
We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...
Let f: ℙ → ℙ be a holomorphic endomorphism of a complex projective space , k ≥ 1, and let J be the Julia set of f (the topological support of the unique maximal entropy measure). Then there exists a positive number such that if ϕ: J → ℝ is a Hölder continuous function with , then ϕ admits a unique equilibrium state on J. This equilibrium state is equivalent to a fixed point of the normalized dual Perron-Frobenius operator. In addition, the dynamical system is K-mixing, whence ergodic. Proving...
This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....
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.