On the structure of an invertible system with a trajectory homoclinic to a saddle-center

DOI10.1007/s10958-007-0352-6zbMath1155.34024OpenAlexW2355624543MaRDI QIDQ942005

O. Yu. Kol'tsova

Publication date: 3 September 2008

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-007-0352-6

zbMATH Keywords

periodic trajectorieshomoclinic trajectoriesinvertible vector fieldssaddle-center singular point

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

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• Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
• Homoclinic orbits in Hamiltonian systems
• Families of multi-round homoclinic and periodic orbits near a saddle-center equilibrium
• Bifurcation of Homoclinic Orbits to a Saddle-Center in Reversible Systems
• Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
• FAMILIES OF TRANSVERSE POINCARÉ HOMOCLINIC ORBITS IN 2N-DIMENSIONAL HAMILTONIAN SYSTEMS CLOSE TO THE SYSTEM WITH A LOOP TO A SADDLE-CENTER
• PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER
• Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems

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