Continuity of the Measure of Maximal Entropy for Unimodal Maps on the Interval

LetT: [0, 1]→[0, 1] be a unimodal map with positive topological entropy. ThenT has a unique measure μ(T) of maximal entropy. It is proved that the mapT↦μ(T) is continuous with respect to the weak star-topology.

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Veröffentlicht in:	Qualitative theory of dynamical systems 2003, Vol.4 (1), p.67-76
1. Verfasser:	Raith, Peter
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Sprache:	eng
Schlagworte:	Entropy Topology
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description	LetT: [0, 1]→[0, 1] be a unimodal map with positive topological entropy. ThenT has a unique measure μ(T) of maximal entropy. It is proved that the mapT↦μ(T) is continuous with respect to the weak star-topology.
doi_str_mv	10.1007/BF02972823
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title	Continuity of the Measure of Maximal Entropy for Unimodal Maps on the Interval
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