Tangencies between stable and unstable manifolds

DOI10.1017/S0308210500014153zbMath0764.34038MaRDI QIDQ4021235

Flaviano Battelli, Kenneth James Palmer

Publication date: 16 January 1993

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

homoclinic orbitsstable and unstable manifoldscompletely integrable dynamical systemsautonomous perturbationfour-dimensional autonomous system

Mathematics Subject Classification ID

Related Items (4)

Computation of bifurcation manifolds of linearly independent homoclinic orbits ⋮ The transversal homoclinic solutions and chaos for stochastic ordinary differential equations ⋮ TRANSVERSE HOMOCLINIC ORBIT BIFURCATED FROM A HOMOCLINIC MANIFOLD BY THE HIGHER ORDER MELNIKOV INTEGRALS ⋮ Multiple chaos arising from single-parametric perturbation of a degenerate homoclinic orbit

Cites Work

• Unnamed Item
• On the existence of separatrix loops in four-dimensional systems similar to the integrable Hamiltonian systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Exponential dichotomies and transversal homoclinic points
• Existence of transversal homoclinic points in a degenerate case
• The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
• Differentiable dynamical systems

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