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

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.