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

V. S. Gonchenko

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 103-119.

Résumé

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.

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