no. 3
Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes
[Dérivée de l’entropie stochastique dans les familles conformes de métriques de courbure strictement négative]
Ledrappier, François1, 2, 3 ; Shu, Lin4
1 CNRS, UMR7599, LPMA F-75005 Paris (France)
2 Department of Mathematics University of Notre-Dame IN 46556-4618 (USA)
3 Sorbonne Universités UPMC Univ. Paris 6, UMR7599, LPMA F-75005 Paris (France)
4 LMAM School of Mathematical Sciences Peking University Beijing 100871 (People’s Republic of China)
Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 1115-1183.

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.

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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3106
Classification : 37D40, 58J65
Keywords: linear drift, negative curvature, stochastic entropy
Mot clés : vitesse de fuite, courbure négative, entropie stochastique

Ledrappier, François 1, 2, 3 ; Shu, Lin 4

1 CNRS, UMR7599, LPMA F-75005 Paris (France)
2 Department of Mathematics University of Notre-Dame IN 46556-4618 (USA)
3 Sorbonne Universités UPMC Univ. Paris 6, UMR7599, LPMA F-75005 Paris (France)
4 LMAM School of Mathematical Sciences Peking University Beijing 100871 (People’s Republic of China)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ledrappier, François; Shu, Lin. Differentiating the stochastic entropy for compact negatively curved spaces under conformal changes. Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 1115-1183. doi : 10.5802/aif.3106. https://aif.centre-mersenne.org/articles/10.5802/aif.3106/

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