Partially hyperbolic diffeomorphisms with uniformly center foliation: the quotient dynamics

2012/10/10 by Doris Bohnet, Christian Bonatti, Bohnet, Doris +1 · 1 citation
Mathematics · Physics and Astronomy · #37C15 #37D30 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C15 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1210.2835

36 pages

openalex publication_date 2012/10/10 · arxiv created 2014/12/10 · arxiv updated 2014/12/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that a partially hyperbolic C¹ -diffeomorphism f : M → M with a uniformly compact f -invariant center foliation F^c is dynamically coherent. Further, the induced homeomorphism F : M/F^c → M/F^c on the quotient space of the center foliation has the shadowing property, i.e. for every ε> 0 there exists δ> 0 such that every δ-pseudo orbit of center leaves is ε-shadowed by an orbit of center leaves. Although the shadowing orbit is not necessarily unique, we prove the density of periodic center leaves inside the chain recurrent set of the quotient dynamics. Some other interesting properties of the quotient dynamics are discussed.

Cited by

• Entropy Flexibility of Dynamical Systems

Related

• Quasi-Shadowing and Quasi-Stability for Dynamically Coherent Partially Hyperbolic Diffeomorphisms
• Partial hyperbolicity and central shadowing
• Codimension one partially hyperbolic diffeomorphisms with a uniformly compact center foliation
• Ergodic properties of partially hyperbolic diffeomorphisms with topological neutral center
• On the plaque topological stability of partially hyperbolic diffeomorphisms