On the Estimation of Topological Entropy on Surfaces

We provide a rigorous lower bound for the topological entropy of planar diffeomorphisms in terms of the geometry of finite pieces of stable and unstable mani- folds of hyperbolic periodic points. Our results suggest the possibility of writing com- puter programs which would automate the estimation of reasonable approximations for the topological entropy of mappings and differential equations. Applying them to the stan- dard Henon map H(x,y )=( 1 +y −ax 2 ,bx) with a = 1.4, b = 0.3 gives the lower bound htop(H) ≥ 0.46469.

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