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Homoclinic bifurcations of endomorphisms: The codimension one case

✍ Scribed by L. Mora

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
473 KB
Volume
11
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this note, we consider the dynamic that appears when we unfold a quadratic degenerate homoclinic point of a generic one-parameter family of endomorphisms fP. This is done through a resealing technique.

Among other facts, it follows from our theorem the abundance of strange expanding sets.

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In this work, bifurcations in the class that the homoclinic orbit connects the strong stable and strong unstable manifolds of a saddle are investigated for four-dimensional vector fields. The existence, numbers, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2 n -homoclinic o