-adic dynamical systems and formal groups
Periodic orbits and chain-transitive sets of C1-diffeomorphisms
We prove that the chain-transitive sets of C1-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C1-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C1-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff topology...
Periodic orbits with least period three on the circle.
Periodic points and dynamic rays of exponential maps.
Periodic points for maps in
Periodic solutions of second order hamiltonian systems bifurcating from infinity
Periods of Morse-Smale diffeomorphisms of 𝕊²
The aim of this paper is to describe the set of periods of a Morse-Smale diffeomorphism of the two-dimensional sphere according to its homotopy class. The main tool for proving this is the Lefschetz fixed point theory.
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...
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.
Prime Orbit Theorems with Multi-Dimensional Constraints for Axiom A Flows.
Puissance extérieure d'un automate déterministe, application au calcul de la fonction zêta d'un système sofique