Let $f$ be a continuous function from $ [0,1] $ to itself with a $3$-period point. How to show that the topology entropy of $f$ is positive?
2026-04-01 02:01:49.1775008909
How to show $3$-period point means positive entropy
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It can be solved by a little improvement of a proof by T.y.Li and J.Yorke showing that "3-peirod implies chaos". Use Markov graph and the concept "$f$-cover" to find a semiconjugate to sybolic system with positive entropy.I find the related theory in Brin and Stuck's book Introduction to Dynamic systems Chapter7.3