Inverse pseudo orbit tracing property for robust diffeomorphisms

2019/07/28 by Manseob Lee, Lee, Manseob
Biochemistry, Genetics and Molecular Biology · Mathematics · #Amino Acid Enzymes and Metabolism #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1907.11995

openalex publication_date 2019/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed smooth Riemannian manifold M, and let f:M→ M be a diffeomorphism. Herein, we demonstrate that (i) if f has the C¹ robustly inverse shadowing property on the chain recurrent set CR(f), then CR(f) is hyperbolic and (ii) if f has the C¹ robustly inverse shadowing property on a nontrivial transitive set Λ⊂ M, then Λ is hyperbolic for f. Especially, the item (ii) is a proof of the conjecture of Lee and Lee \citeLL.

Related

• Inverse periodic shadowing properties
• Robustly shadowable chain transtive sets and hyperbolicity
• Characterization of hyperbolicity and generalized shadowing lemma
• Partial hyperbolicity and central shadowing
• Quasi-Shadowing and Quasi-Stability for Dynamically Coherent Partially Hyperbolic Diffeomorphisms