Homoclinic Bifurcations for the Henon Map

Details Homoclinic Bifurcations for the Henon Map Homoclinic Bifurcations for the Henon Map

1999-04-09

arxiv.org/abs/chao-dyn/9904019v1

Physica D, 134:153--184, 1999

Nonlinear Sciences

Chaotic Dynamics

To appear in PhysicaD: 43 Pages, 14 figures

Scientific paper

10.1016/S0167-2789(99)00125-6

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use 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 horseshoe as well as a subshift of finite type. We classify homoclinic bifurcations, and study those for the area preserving case in detail. Simple forcing relations between homoclinic orbits are established. We show that a symmetry of the map gives rise to constraints on certain sequences of homoclinic bifurcations. Our numerical studies also identify the bifurcations that bound intervals on which the topological entropy is apparently constant.

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