Vanishing transverse entropy in smooth ergodic theory

Vanishing transverse entropy in smooth ergodic theory

For a measure-preserving transformation, the entropy being zero means that there is no increasing σ-algebra. In this note, we prove that a similar phenomenon occurs for C2 diffeomorphisms when considering the increment between the partial entropies associated with different exponents.

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Veröffentlicht in:Ergodic theory and dynamical systems 2011-08, Vol.31 (4), p.1229-1235
Hauptverfasser: LEDRAPPIER, FRANÇOIS, XIE, JIAN-SHENG
Format: Artikel
Sprache:eng
Schlagworte:
Dynamical systems
Entropy
Entropy of transformation
Ergodic processes
Exponents
Mathematics
Probability
Transformations
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Beschreibung
Zusammenfassung:For a measure-preserving transformation, the entropy being zero means that there is no increasing σ-algebra. In this note, we prove that a similar phenomenon occurs for C2 diffeomorphisms when considering the increment between the partial entropies associated with different exponents.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385710000416