Shadowing for codimension one sectional-Anosov flows
Dynamical Systems
2020-06-26 v1
Abstract
In hyperbolic dynamics, a well-known result is that every hyperbolic attracting set, have a finite pseudo-orbit tracing property (FPOTP). It's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics; Komuro in [Lorenz attractors do not have the pseudo-orbit tracing property], provides a negative answer for this question, by proving that the geometric Lorenz Attractor doesn't have a FPOTP. In this paper, we generalized the result of Komuro, we prove that every codimension one sectional-hyperbolic attractor set with a unique singularity Lorenz-like, which is of boundary-type, does not have FPOTP.
Cite
@article{arxiv.2006.14369,
title = {Shadowing for codimension one sectional-Anosov flows},
author = {A. Arbieto and A. M. López and Y. Sánchez},
journal= {arXiv preprint arXiv:2006.14369},
year = {2020}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:1804.01412