Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows

Continuity of topological entropy for perturbation of time-one maps of hyperbolic flows

We consider a C 1 neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for all known examples of partially hyperbolic diffeomorphisms with...

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Veröffentlicht in:Israel journal of mathematics 2016-09, Vol.215 (2), p.857-875
Hauptverfasser: Saghin, Radu, Yang, Jiagang
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Chaos theory
Continuity (mathematics)
Entropy
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Zusammenfassung:We consider a C 1 neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for all known examples of partially hyperbolic diffeomorphisms with one-dimensional center bundle.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1396-4