Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions

DOI10.3934/dcds.2021010zbMath1470.37037arXiv2006.01405OpenAlexW3120415512MaRDI QIDQ2030789

David J. W. Simpson, Sishu Shankar Muni, Robert I. Mclachlan

Publication date: 8 June 2021

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.01405

zbMATH Keywords

periodic solutionshomoclinic tangencymultistabilityasymptotically stablesmooth maps

Mathematics Subject Classification ID

Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Stability theory for smooth dynamical systems (37C75) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (1)

Unfolding globally resonant homoclinic tangencies

Cites Work

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• On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies
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• Diffeomorphisms with infinitely many sinks
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• Sequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form
• On dynamics and bifurcations of area-preserving maps with homoclinic tangencies
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
• Unfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• Generalized Hénon Map and Bifurcations of Homoclinic Tangencies
• Subsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps
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