Abstract
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.
Original language | English |
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Pages (from-to) | 1245-1270 |
Number of pages | 26 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 37 |
Issue number | 6 |
DOIs | |
State | Published - 1 Nov 2020 |
Keywords
- Lyapunov exponents
- Partial hyperbolicity
- SRB measures
- Stable ergodicity
- Statistical stability