An "Observable" horseshoe map

Xu Zhang; Yukai Wang; Guanrong Chen

doi:10.1063/5.0188700

An "Observable" horseshoe map

Chaos. 2024 Feb 1;34(2):021106. doi: 10.1063/5.0188700.

Authors

Xu Zhang¹, Yukai Wang¹, Guanrong Chen²

Affiliations

¹ Department of Mathematics, Shandong University, Weihai, Shandong 264209, China.
² Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China.

PMID: 38421854
DOI: 10.1063/5.0188700

Abstract

In this article, a family of diffeomorphisms with growing horseshoes contained in global attracting regions is presented, where the dimension of the unstable direction can be any fixed integer and a growing horseshoe means that the number of the folds of the horseshoe is increasing as a parameter is varied. Moreover, it is demonstrated that the horseshoe-like attractors are observable for certain parameters.