Low dimensional bifurcations of snap-back repellors

Abstract

We study the relationship between homoclinic orbits associated to repellors, usually called snap-back repellors, and expanding sets of smooth endomorphisms. Critical homoclinic orbits constitutes an interesting bifurcation that is locally contained in the boundary of the set of maps having homoclinic orbits. This and other possible routes to the creation of homoclinic orbits are considered in low dimensions.