No-shadowing for singular hyperbolic sets with a singularity
Dynamical Systems
2020-03-12 v1
Abstract
We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star flow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.
Keywords
Cite
@article{arxiv.2003.05165,
title = {No-shadowing for singular hyperbolic sets with a singularity},
author = {Xiao Wen and Lan Wen},
journal= {arXiv preprint arXiv:2003.05165},
year = {2020}
}