Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes

Abstract

AbstractIn this paper, we propose a model for the destruction of three-dimensional horseshoes via heterodimensional cycles. This model yields some new dynamical features. Among other things, it provides examples of homoclinic classes properly contained in other classes and it is a model of a new sort of heteroclinic bifurcations we callgenerating.