Invariant Sets and Hyperbolic Closed Reeb Orbits - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Invariant Sets and Hyperbolic Closed Reeb Orbits

Résumé

We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbit on the dynamics of a Reeb flow on the $(2n-1)$-dimensional standard contact sphere, extending two results previously known for Hamiltonian diffeomorphisms to the Reeb setting. In particular, we show that under very mild dynamical convexity type assumptions, the presence of one hyperbolic closed orbit implies the existence of infinitely many simple closed Reeb orbits. The second main result of the paper is a higher-dimensional Reeb analogue of the Le Calvez-Yoccoz theorem, asserting that no closed orbit of a non-degenerate dynamically convex Reeb pseudo-rotation is locally maximal, i.e., isolated as an invariant set. The key new ingredient of the proofs is a Reeb variant of the crossing energy theorem.

Dates et versions

hal-04225749 , version 1 (03-10-2023)

Identifiants

Citer

Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. Invariant Sets and Hyperbolic Closed Reeb Orbits. 2023. ⟨hal-04225749⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More