Generalized Attracting Horseshoes and Chaotic Strange Attractors
Dynamical Systems
2020-12-09 v2
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.
Keywords
Cite
@article{arxiv.1611.04133,
title = {Generalized Attracting Horseshoes and Chaotic Strange Attractors},
author = {Yogesh Joshi and Denis Blackmore and Aminur Rahman},
journal= {arXiv preprint arXiv:1611.04133},
year = {2020}
}
Comments
8 pages, 4 figures