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Cascades of reversible homoclinic orbits to a saddle-focus equilibrium

✍ Scribed by Jörg Härterich

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
893 KB
Volume
112
Category
Article
ISSN
0167-2789

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✦ Synopsis

In a reversible system, we consider a homoclinic orbit being bi-asymptotic to a saddle-focus equilibrium. As was proved by , there exists a one-parameter family of periodic orbits accumulating onto this homoclinic orbit.

In the present paper, we show that for any n > 2 there exist infinitely many n-homoclinic orbits in a neighborhood of the primary homoclinic orbit. Each of them is accompanied by one or more families of periodic orbits. Moreover, we indicate how these families of periodic orbits correspond to branches of subharmonic periodic orbits.

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Homoclinic orbits to invariant tori near
Homoclinic orbits to invariant tori near a homoclinic orbit to center–center–saddle equilibrium
✍ Oksana Koltsova; Lev Lerman; Amadeu Delshams; Pere Gutiérrez 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 257 KB

We consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center-center-saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based on the unperturbed homoclinic loop), we study the homoclinic intersections betwe