Periodic orbits of renormalisation for the correlations of strange nonchaotic attractors.
Periodic orbits with least period three on the circle.
Periodic points for maps in
Periodic points of Hamiltonian surface diffeomorphisms.
Persistence of fixed points under rigid perturbations of maps
Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving homeomorphisms...
Persistence of homoclinic tangencies for area-preserving maps
Pesin theory and equilibrium measures on the interval
We use Pesin theory to study possible equilibrium measures for a broad class of piecewise monotone maps of the interval and a broad class of potentials.
Plane affine geometry and Anosov flows
Polynomial decay of correlations for a class of smooth flows on the two torus
Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a -speed of mixing, for some .
Position dependent random maps in one and higher dimensions
A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of ℝⁿ. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of ℝⁿ are the main results.
Positive Lyapunov exponents in families of one dimensional dynamical systems.
Potentials unbounded below.
Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour de certains points fixes ?
Soit un homéomorphisme du plan qui préserve l’orientation et qui a un point périodique de période . Nous montrons qu’il existe un point fixe tel que le nombre d’enlacement de et ne soit pas nul. En d’autres termes, le nombre de rotation de l’orbite de dans l’anneau est un élément non nul de . Ceci donne une réponse positive à une question posée par John Franks.
Powers and alternative laws
A groupoid is alternative if it satisfies the alternative laws and . These laws induce four partial maps on
Propriétés ergodiques du flot horocyclique d'une surface hyperbolique géométriquement finie
Propriétés générales des applications déviant la verticale
Pruning theory and Thurston's classification of surface homeomorphisms
Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading – both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy.
Puissance extérieure d'un automate déterministe, application au calcul de la fonction zêta d'un système sofique
Quadratic regular reversal maps.
Quasi-morphismes et invariant de Calabi