Cruising in a central force field.
We give a description of possible sets of cycle lengths for distance-decreasing maps and isometries of the ring of n-adic integers.
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.
Utilisant le Théorème de Normalisation de Mourtada (Lect. Notes. in Math., no 1445, pp. 272-314), on montre que les polycycles hyperboliques et génériques sont de cyclicité finie dans les familles de champs de vecteurs du plan. Ceci implique que le 16e problème de Hilbert est localement vrai sur un ouvert dense dans l’espace des champs de vecteurs polynomiaux du plan de degré .
The main results of this paper are: 1. No topologically transitive cocycle -extension of minimal rotation on the unit circle by a continuous real-valued bounded variation ℤ-cocycle admits minimal subsets. 2. A minimal rotation on a compact metric monothetic group does not admit a topologically transitive real-valued cocycle if and only if the group is finite.
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in .