Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes
Annales de l'Institut Fourier, Volume 67 (2017) no. 3, p. 1115-1183

We consider the universal cover of a closed connected Riemannian manifold of negative sectional curvature. We show that the linear drift and the stochastic entropy are differentiable under any ${C}^{3}$ one-parameter family of ${C}^{3}$ conformal changes of the original metric.

Nous considérons le revêtement universel d’une variété compacte connexe de courbure strictement négative et une variation à un paramètre de classe ${C}^{3}$ de métriques ${C}^{3}$ conformes à la métrique originale. Nous montrons que la vitesse de fuite et l’entropie stochastique sont différentiables le long de cette courbe.

Revised : 2015-08-11
Accepted : 2016-09-16
Published online : 2017-05-31
DOI : https://doi.org/10.5802/aif.3106
Classification:  37D40,  58J65
Keywords: linear drift, negative curvature, stochastic entropy
@article{AIF_2017__67_3_1115_0,
author = {Ledrappier, Fran\c cois and Shu, Lin},
title = {Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {67},
number = {3},
year = {2017},
pages = {1115-1183},
doi = {10.5802/aif.3106},
language = {en},
url = {http://www.numdam.org/item/AIF_2017__67_3_1115_0}
}

Ledrappier, François; Shu, Lin. Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes. Annales de l'Institut Fourier, Volume 67 (2017) no. 3, pp. 1115-1183. doi : 10.5802/aif.3106. http://www.numdam.org/item/AIF_2017__67_3_1115_0/

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