TY - JOUR
T1 - Statistical stability of mostly expanding diffeomorphisms
AU - Andersson, Martin
AU - VASQUEZ EHRENFELD, CARLOS
N1 - Publisher Copyright:
© 2020 L'Association Publications de l'Institut Henri Poincaré
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - We study how physical measures vary with the underlying dynamics in the open class of Cr, r>1, strong partially hyperbolic diffeomorphisms for which the central Lyapunov exponents of every Gibbs u-state is positive. If transitive, such a diffeomorphism has a unique physical measure that persists and varies continuously with the dynamics. A main ingredient in the proof is a new Pliss-like Lemma which, under the right circumstances, yields frequency of hyperbolic times close to one. Another novelty is the introduction of a new characterization of Gibbs cu-states. Both of these may be of independent interest. The non-transitive case is also treated: here the number of physical measures varies upper semi-continuously with the diffeomorphism, and physical measures vary continuously whenever possible.
AB - We study how physical measures vary with the underlying dynamics in the open class of Cr, r>1, strong partially hyperbolic diffeomorphisms for which the central Lyapunov exponents of every Gibbs u-state is positive. If transitive, such a diffeomorphism has a unique physical measure that persists and varies continuously with the dynamics. A main ingredient in the proof is a new Pliss-like Lemma which, under the right circumstances, yields frequency of hyperbolic times close to one. Another novelty is the introduction of a new characterization of Gibbs cu-states. Both of these may be of independent interest. The non-transitive case is also treated: here the number of physical measures varies upper semi-continuously with the diffeomorphism, and physical measures vary continuously whenever possible.
KW - Lyapunov exponents
KW - Partial hyperbolicity
KW - SRB measures
KW - Stable ergodicity
KW - Statistical stability
UR - http://www.scopus.com/inward/record.url?scp=85087658929&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2020.04.007
DO - 10.1016/j.anihpc.2020.04.007
M3 - Article
AN - SCOPUS:85087658929
VL - 37
SP - 1245
EP - 1270
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
SN - 0294-1449
IS - 6
ER -