On the Estimation of Topological Entropy on Surfaces
AbstractWe provide a rigorous lower bound for the topological entropy of planar diffeomorphisms
in terms of the geometry of finite pieces of stable and unstable manifolds of hyperbolic periodic points.
Our results suggest the possibility of writing computer programs which would automate the
estimation of reasonable approximations for the topological entropy of mappings and differential equations.
Applying them to the standard Henon map H(x, y) = (1 + y - ax^2 , bx) with a = 1.4, b = 0.3 gives
the lower bound h(H) >= 0.46469.
S. Newhouse, M. Berz, J. Grote, K. Makino,
Contemporary Mathematics 469 (2008) 243-270
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