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

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
Format: Artikel
Sprache:eng
Schlagworte:
Entropy
Topology
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Zusammenfassung: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.
ISSN:1662-3592
1575-5460
1662-3592
DOI:10.1007/BF02972823