Cycles of distance-decreasing mappings in the ring of n-adic integers
We give a description of possible sets of cycle lengths for distance-decreasing maps and isometries of the ring of n-adic integers.
Cycles of links and fixed points for orientation preserving homeomorphisms of the open unit disk
Michael Handel proved the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel's theorem to a wider class of cycles of links. In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.
Decay of correlations in one-dimensional dynamics
Decay of geometry for Fibonacci critical covering maps of the circle
Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo)
Decompositions of Factor Maps Involving Bi-closing Maps.
Density of periodic orbit measures for transformations on the interval with two monotonic pieces
Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and , it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.
Derivatives of circle rotations, and similarity of orbits.
Déviations de moyennes ergodiques, flots de Teichmüller et cocycle de Kontsevich-Zorich
Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...
Different types of scaling in the dynamics of period-doubling maps under external periodic driving.
Differentiable rigidity and smooth conjugacy.
Dimension groups for interval maps.
Dimension of weakly expanding points for quadratic maps
For the real quadratic map and a given a point has good expansion properties if any interval containing also contains a neighborhood of with univalent, with bounded distortion and for some . The -weakly expanding set is the set of points which do not have good expansion properties. Let denote the negative fixed point and the first return time of the critical orbit to . We show there is a set of parameters with positive Lebesgue measure for which the Hausdorff dimension of...
Diophantine classes, dimension and Denjoy maps
Discrete anisotropic curvature flow of graphs
Discrete anisotropic curvature flow of graphs
The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.
Dispersion properties of ergodic translations.
Distortion bounds for unimodal maps
We obtain estimates for derivative and cross-ratio distortion for (any η > 0) unimodal maps with non-flat critical points. We do not require any “Schwarzian-like” condition. For two intervals J ⊂ T, the cross-ratio is defined as the value B(T,J): = (|T| |J|)/(|L| |R|) where L,R are the left and right connected components of T∖J respectively. For an interval map g such that is a diffeomorphism, we consider the cross-ratio distortion to be B(g,T,J): = B(g(T),g(J))/B(T,J). We prove that for...
Distributional chaos for flows
Schweizer and Smítal introduced the distributional chaos for continuous maps of the interval in B. Schweizer, J. Smítal, Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Amer. Math. Soc. 344 (1994), 737–854. In this paper, we discuss the distributional chaos DC1–DC3 for flows on compact metric spaces. We prove that both the distributional chaos DC1 and DC2 of a flow are equivalent to the time-1 maps and so some properties of DC1 and DC2 for discrete systems...
Distributional chaos on tree maps: the star case
Let , , and let be a continuous map having the branching point fixed. We prove that is distributionally chaotic iff the topological entropy of is positive.