Abstract
Topological invariants of the Henon map are investigated by means of the pruning front. First, a long sequence of primary homoclinic tangencies is computed, confirming the monotonicity of the front. An algorithm to extract forbidden sequences is then introduced and discussed. Forbidden sequences of increasing lengths are used to construct a hierarchy of regular grammars, represented by directed graphs, which approximate the exact grammar arbitrarily well. The topological entropy is estimated as the largest eigenvalue of their adjacency matrix. It exhibits an exponential convergence towards the asymptotic value with an exponent in agreement with a previous conjecture based on the growth rate of the number of forbidden words.
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