Inclination-flip homoclinic orbits arising from orbit-flip

Citation
Ca. Morales et Mj. Pacifico, Inclination-flip homoclinic orbits arising from orbit-flip, NONLINEARIT, 14(2), 2001, pp. 379-393
Citations number
8
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
14
Issue
2
Year of publication
2001
Pages
379 - 393
Database
ISI
SICI code
0951-7715(200103)14:2<379:IHOAFO>2.0.ZU;2-O
Abstract
sigma egenerated homoclinic orbits for C-1 hows on closed 3-manifolds are s tudied. We assume that Gamma, the homoclinic orbit, is associated with a si ngularity sigma with real eigenvalues lambda (2) < <lambda>(3) < 0 < lambda (1). Degenerated means that either the centre-unstable and stable manifold s of sigma are tangent along Gamma (inclination-flip) or Gamma belongs to t he strong stable manifold of sigma (orbit-flip). We prove that if Gamma is orbit-flip, and -lambda (2) < <lambda>(1), then the corresponding vector he ld can be C-1 approximated by those exhibiting inclination-flip homoclinic orbits.