Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria

Abstract

In this chapter we will study global bifurcations corresponding to the appearance of homoclinic or heteroclinic orbits connecting hyperbolic equilibria in continuous-time dynamical systems. First we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic n-dimensional cases to the considered ones plus a four-dimensional case. This remaining case is treated in Appendix 1.