The entropy conjecture for diffeomorphisms away from tangencies

Liao, Gang, Viana, Marcelo, and Yang, Jiagang. "The entropy conjecture for diffeomorphisms away from tangencies." Journal of the European Mathematical Society 015.6 (2013): 2043-2060. <http://eudml.org/doc/277328>.

@article{Liao2013,
abstract = {We prove that every $C^1$ 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.},
author = {Liao, Gang, Viana, Marcelo, Yang, Jiagang},
journal = {Journal of the European Mathematical Society},
keywords = {entropy conjecture; principal symbolic extensions; upper semi-continuity of the entropy; homoclinic tangencies; entropy conjecture; principal symbolic extensions; upper semi-continuity of the entropy; homoclinic tangencies},
language = {eng},
number = {6},
pages = {2043-2060},
publisher = {European Mathematical Society Publishing House},
title = {The entropy conjecture for diffeomorphisms away from tangencies},
url = {http://eudml.org/doc/277328},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Liao, Gang
AU - Viana, Marcelo
AU - Yang, Jiagang
TI - The entropy conjecture for diffeomorphisms away from tangencies
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 2043
EP - 2060
AB - We prove that every $C^1$ 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.
LA - eng
KW - entropy conjecture; principal symbolic extensions; upper semi-continuity of the entropy; homoclinic tangencies; entropy conjecture; principal symbolic extensions; upper semi-continuity of the entropy; homoclinic tangencies
UR - http://eudml.org/doc/277328
ER -