The Entropy Conjecture for Diffeomorphisms away from Tangencies
By Li Gang, Marcelo Viana, Jiagang Yang. 2010
92 citations recorded by the source corpus.
We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub's entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive and have no symbolic extensions.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/422308b4db0f81c06264c228986164cf641a365d
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In Geometry and Topology
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Citations in the corpus
- Entropy along expanding foliations (2016, background): “The research on the regularity of entropy has a long history, one can find more references from [37, 26, 23, 34, 36].”