Low-Dimensional Homoclinic Bifurcations of Repellers

Abstract

We study the relationship between homoclinic orbits associated with repellers, usually called snap-back repellers, and expanding sets of smooth endomorphisms. We also consider critical homoclinic orbits and prove that the bifurcations they create constitute a codimension one phenomenon. This and other possible routes to the creation of homoclinic orbits are considered in low dimensions.