The Transverse Homoclinic Dynamics and their Bifurcations at Nonhyperbolic Fixed Points

DOI10.2307/2153995zbMath0766.34028OpenAlexW4252579448MaRDI QIDQ3993841

Bo Deng

Publication date: 13 August 1992

Full work available at URL: https://doi.org/10.2307/2153995

zbMATH Keywords

diffeomorphismsaddle-node bifurcationdynamicsorbittransversehomoclinichyperbolic fixed pointnet weaving bifurcation

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Applications of dynamical systems (37N99) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (2)

Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points ⋮ Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies

Cites Work

• Unnamed Item
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• Global bifurcations and chaos. Analytical methods
• Diffeomorphisms with infinitely many sinks
• Stable and Random Motions in Dynamical Systems
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• Melnikov’s Method at a Saddle-Node and the Dynamics of the Forced Josephson Junction
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• Differentiable dynamical systems
• ON A POINCARÉ-BIRKHOFF PROBLEM
• Invariant manifolds

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