This article is cited in 2 papers

Homoclinic Tangencies, $\Omega$-Moduli, and Bifurcations

V. S. Gonchenko

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: A survey of author's results related to the problems of existence of continuous invariants (moduli) of $\Omega$-conjugacy of multidimensional diffeomorphisms with homoclinic tangencies is presented. The problem of bifurcations of periodic orbits is considered in the case of four-dimensional diffeomorphisms with a nontransversal homoclinic orbit to a fixed point of saddle–focus type.

UDC: 517.9

Received in February 2001

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 94–109

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