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Common terms and phrasesapproximation asymptotic behavior attractor billiard map binary Birkhoff periodic orbits boundary Cantor set closed compact complexity conjugacy consider constant continuous function continuous map Contraction Principle converge convex coordinate corresponding curves cylinder defined Definition dense described differential equations digits disjoint dynamical systems eigenvalues elliptic endpoints equivalent Euclidean example Exercise exists expanding maps exponential Figure finite flow geodesic gives hence homeomorphism homoclinic horseshoe hyperbolic set implies integral intersection interval invariant circle invertible irrational rotation iterates Lemma length linear map mathematical matrix measure metric space minimal norm null set obtained open set parameter periodic orbits periodic points phase space preimages Problem Proof Proposition Prove rational rectangle recurrent Riemann integrable rotation number Section sequence solutions subset Theorem topological entropy topological Markov chain topologically mixing topologically transitive torus twist map uniform distribution uniformly unique ergodicity values vector zero References to this bookFrom other books
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