This article is cited in 4 papers

An example of a resonant homoclinic loop of infinite cyclicity

D. V. Turaev

Ben-Gurion University of the Negev

Abstract: We describe a codimension-3 bifurcation surface in the space of $C^r$-smooth ($r\ge 3$) dynamical systems (with phase space of dimension 4 or higher) having an attractive two-dimensional invariant manifold with an infinite sequence of periodic orbits of alternating stability which converge to a homoclinic loop.

Key words and phrases: Codimension-3 homoclinic bifurcation, invariant manifold, swallow tail, limit cycle.

MSC: 37G20, 34C07, 34C37

Received: April 7, 2003

Language: English

DOI: 10.17323/1609-4514-2005-5-1-283-293

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