Z. Galias et P. Zgliczynski, Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon map, NONLINEARIT, 14(5), 2001, pp. 909-932
We show how to link topological tools with a local hyperbolic behaviour to
prove the existence of homoclinic and heteroclinic trajectories for a map.
We apply this technique for the Henon map h with classical parameter values
(a = 1.4, b = 0.3). For this map we give a computer-assisted proof of the
existence of an infinite number of homoclinic and heteroclinic trajectories
. We also introduce the method for computation of the lower bound of the to
pological entropy of a map based on the covering relations involving differ
ent iterations of the map and we prove that the topological entropy of h is
larger than 0.3381.