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arXiv · 1611.04133

Generalized Attracting Horseshoes and Chaotic Strange Attractors

Yogesh Joshi·Denis Blackmore·Aminur Rahman
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Abstract

A generalized attracting horseshoe is introduced as a new paradigm for describing chaotic strange attractors (of arbitrary finite rank) for smooth and piecewise smooth maps f from Q to Q, where Q is a homeomorph of the unit interval in real m-space for any integer m > 1. The main theorems for generalized attracting horseshoes are shown to apply to Henon and Lozi maps, thereby leading to rather simple new chaotic strange attractor existence proofs that apply to a range of parameter values that includes those of earlier proofs.

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Yogesh Joshi, Denis Blackmore, Aminur Rahman. 2016-11-13. Generalized Attracting Horseshoes and Chaotic Strange Attractors. https://arxiv.org/abs/1611.04133

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