Homoclinic classes with shadowing property

2011/01/07 by Lee, Manseob
#37C05 #37C20 #37C29 #37D05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.1348

Abstract

We show that for C¹ generic diffeomorphisms, an isolated homoclinic class is shadowable if and only if homoclinic class is hyperbolic basic set.

Related

• Generic homeomorphisms with shadowing of one-dimensional continua
• Codimension one generic homoclinic classes with interior
• Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes
• On the hyperbolicity of C¹-generic homoclinic classes
• Partial hyperbolicity and central shadowing