BIFURCATIONS OF SNAP-BACK REPELLERS WITH APPLICATION TO BORDER-COLLISION BIFURCATIONS

DOI10.1142/S0218127410025557zbMath1188.37051OpenAlexW2075333188MaRDI QIDQ3567263

Paul Glendinning

Publication date: 11 June 2010

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

Full work available at URL: https://doi.org/10.1142/s0218127410025557

zbMATH Keywords

hybrid systemborder-collision bifurcationsnap-back-repeller

Mathematics Subject Classification ID

Low-dimensional dynamical systems (37E99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (5)

Sequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form ⋮ Critical homoclinic orbits lead to snap-back repellers ⋮ Analysis of Snapback Repellers Using Methods of Symbolic Computation ⋮ Border-Collision Bifurcations in $\mathbb{R}^N$ ⋮ Algebraic Analysis of Bifurcations and Chaos for Discrete Dynamical Systems

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Border-collision bifurcations including ``period two to period three for piecewise smooth systems
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• An improved version of the Marotto theorem
• Chaos induced by regular snap-back repellers
• On redefining a snap-back repeller
• HETEROCLINICAL REPELLERS IMPLY CHAOS
• Robust Chaos
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
• Snap-back repellers and scrambled sets in general topological spaces

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