Geodesic
The entropy conjecture for diffeomorphisms away from tangencies
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2043-2060

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/413
Classification : 37-XX
Keywords: entropy conjecture, principal symbolic extensions, upper semi-continuity of the entropy, homoclinic tangencies 
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     title = {The entropy conjecture for diffeomorphisms away from tangencies},
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Gang Liao; Marcelo Viana; Jiagang Yang. The entropy conjecture for diffeomorphisms away from tangencies. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2043-2060. doi: 10.4171/jems/413

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