THE PERSISTENCE OF SNAP-BACK REPELLER UNDER SMALL C1 PERTURBATIONS IN BANACH SPACES

DOI10.1142/S0218127411028702zbMath1215.37021OpenAlexW1976608642MaRDI QIDQ3010310

YuanLong Chen, Liangliang Li, Yu Huang

Publication date: 30 June 2011

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127411028702

zbMATH Keywords

snap-back repellerimplicit function theoremDevaney's chaos

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (8)

Chaos on discrete neural network loops with self-feedback ⋮ Complex dynamics of a delayed discrete neural network of two nonidentical neurons ⋮ Chaos for implicit difference equations with snap-back repellers ⋮ The Structural Stability of Maps with Heteroclinic Repellers ⋮ Heteroclinic cycles imply chaos and are structurally stable ⋮ The \(C^1\) persistence of heteroclinic repellers in \(\mathbb{R}^n\) ⋮ Chaotic Dynamics of Discrete Multiple-Time Delayed Neural Networks of Ring Architecture Evoked by External Inputs ⋮ Complex Dynamics of Discrete-Time Ring Neural Networks

Cites Work

• Unnamed Item
• Unnamed Item
• Chaotic behavior in the Henon mapping
• A simple proof for persistence of snap-back repellers
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Chaos of discrete dynamical systems in complete metric spaces
• On redefining a snap-back repeller
• Discrete chaos in Banach spaces
• Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps
• On Devaney's Definition of Chaos
• Period Three Implies Chaos
• Snapback repellers as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span
• Devaney's chaos or 2-scattering implies Li-Yorke's chaos

This page was built for publication: THE PERSISTENCE OF SNAP-BACK REPELLER UNDER SMALL C¹ PERTURBATIONS IN BANACH SPACES