The entropy conjecture for diffeomorphisms away from tangencies
Marcelo Viana
IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, BrazilGang Liao
Peking University, Beijing, ChinaJiagang Yang
Universidade Federal Fluminense - UFF, Niterói, Brazil

Abstract
We prove that every 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.
Cite this article
Marcelo Viana, Gang Liao, Jiagang Yang, The entropy conjecture for diffeomorphisms away from tangencies. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2043–2060
DOI 10.4171/JEMS/413