On the quasi-hyperbolic regime in a certain family of 2-D piecewise linear maps

Abstract

The main goal of this paper is to offer a proof of quasi-hyperbolicity in a certain family of 2-D piecewise linear maps by applying the theorem of Shilnikov and Gavrilov concerning the hyperbolicity of some types of smooth maps.

Keywords:

• Piecewise smooth map
• normal form
• hyperbolic attractor
• quasi-hyperbolic attractor

2020 Mathematics Subject Classification:

• 65P20

Acknowledgments

The authors wish to acknowledge the editor and anonymous reviewers for their insightful comments, which have improved the quality of this publication.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Directorate-General for Scientific Research and Technological Development of Algeria (DGRSDT).