ISSN:
1572-9222
Keywords:
homoclinic obit
;
bifurcation
;
Conley index
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We study bifurcations, calledN-homoclinic bifurcations, which produce homoclinic orbits roundingN times (N⩾2) in some tubular neighborhood of original homoclinic orbit. A family of vector fields undergoes such a bifurcation when it is a perturbation of a vector field with a homoclinic orbit.N-Homoclinic bifurcations are divided into two cases; one is that the linearization at the equilibrium has only real principal eigenvalues, and the other is that it has complex principal eigenvalues. We treat the former case, espcially that linearization has only one unstable eigenvalue. As main tools we use a topological method, namely, Conley index theory, which enables us to treat more degenerate cases than those studied by analytical methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02218844
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