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Continuity of entropy for Lorenz maps. (English) Zbl 1437.37049

The authors consider a one-parameter family of expanding interval maps \(\{T_p\}\) with two increasing continuous branches and discontinuity at \(p\). P. Raith [Commentat. Math. Univ. Carol. 41, No. 1, 61–78 (2000; Zbl 1034.37021)] proved that the topological entropy of \(T_p\) varies continuously as a function of \(p\). The present paper provides an alternative proof using Milnor-Thurston kneading theory.

MSC:

37E05 Dynamical systems involving maps of the interval
37B40 Topological entropy

Citations:

Zbl 1034.37021
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References:

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