Generalized Attracting Horseshoes and Chaotic Strange Attractors

2016/11/13 by Yogesh M. Joshi, Joshi, Yogesh, Denis Blackmore +3
Mathematics · Physics and Astronomy · #37D45 #37E99 #92D25 #92D40 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1611.04133

openalex publication_date 2016/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Periodic orbits as the skeleton of classical and quantum chaos
• Deterministic Nonperiodic Flow

Related

• Elements of contemporary mathematical theory of dynamical chaos. Part 1. Pseudohyperbolic attractors
• Existence of an attractor and Horseshoe in multidimensional Hénon map
• Invariant cones for strange attractors of Lozi, Hénon and Belykh type maps
• Abundance of weird quasiperiodic attractors in piecewise linear discontinuous maps
• Strange attractors for the family of orientation preserving Lozi maps