Homoclinic bifurcations for the Henon map

Chaotic dynamics can be effectively studied by continuation from an anti-in tegrable limit. We use this limit to assign global symbols to orbits and us e continuation from the limit to study their bifurcations. We find a bound on the parameter range for which the Henon map exhibits a complete binary h orseshoe as well as a subshift of finite type. We classify homoclinic bifur cations, and study those for the area preserving case in detail. Simple for cing relations between homoclinic orbits are established. We show that a sy mmetry of the map gives rise to constraints on certain sequences of homocli nic bifurcations. Our numerical studies also identify the bifurcations that bound intervals on which the topological entropy is apparently constant. ( C) 1999 Elsevier Science B.V. All rights reserved. MSC; 58F05; 58F03; 58C15 .