Heteroclinic orbits in singular systems: A unifying approach

DOI10.1007/BF02219191zbMath0804.34047MaRDI QIDQ1319928

Flaviano Battelli

Publication date: 24 January 1995

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

bifurcationsingularly perturbed systemexistence of heteroclinic orbitsmanifolds of hyperbolic fixed points

Mathematics Subject Classification ID

Asymptotic properties of solutions to ordinary differential equations (34D05) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

Transversality of homoclinic orbits and exponential dichotomies for parabolic equations ⋮ Construction and asymptotic stability of structurally stable internal layer solutions ⋮ Transverse intersection of invariant manifolds in singular systems. ⋮ Heteroclinic orbits in singular systems: A unifying approach. Addendum ⋮ Chaotic traveling wave solutions in coupled Chua's circuits ⋮ Transversal bounded solutions in systems with normal slow variables

Cites Work

• Unnamed Item
• Heteroclinic orbits in systems with slowly varying coefficients
• Transversal heteroclinic and homoclinic orbits in singular perturbation problems
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Geometric singular perturbation theory for ordinary differential equations
• Global bifurcations and chaos. Analytical methods
• Chaos in the Duffing equation
• Asymptotic solutions of analytic Hamiltonian systems
• Existence of transversal homoclinic points in a degenerate case
• Shadowing Lemma and Singularly Perturbed Boundary Value Problems
• Invariant manifolds in singular perturbation problems for ordinary differential equations

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