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arXiv · 2006.14369

Shadowing for codimension one sectional-Anosov flows

A. Arbieto·A. M. López·Y. Sánchez
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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.

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A. Arbieto, A. M. López, Y. Sánchez. 2020-06-23. Shadowing for codimension one sectional-Anosov flows. https://arxiv.org/abs/2006.14369

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