Diabolical Entropy

Diabolical Entropy

Milnor and Thurston’s famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is Hölder continuous. We obtain a precise formula for the Hölder exponent at almost every quadratic parameter. Furthermore, the entropy at most parameters is p...

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Veröffentlicht in:Communications in mathematical physics 2019-02, Vol.365 (3), p.1091-1123
Hauptverfasser: Dobbs, Neil, Mihalache, Nicolae
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Dynamical Systems
Entropy
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Parameters
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Zusammenfassung:Milnor and Thurston’s famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is Hölder continuous. We obtain a precise formula for the Hölder exponent at almost every quadratic parameter. Furthermore, the entropy at most parameters is proven to be in a set of Hausdorff dimension smaller than one, while most values of the entropy arise from a set of parameters of dimension smaller than one.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03293-y