Statistical stability for robust classes of maps with non-uniform expansion
By José F. Alves, Marcelo Viana. Ergodic Theory and Dynamical Systems, 2000
134 citations recorded by the source corpus.
We consider open sets of transformations in a manifold M, exhibiting non-uniformly expanding behavior in some forward invariant domain U\subset M. Assuming that each transformation has a unique Sinai–Ruelle–Bowen (SRB) measure in U, and some general uniformity conditions, we prove that the SRB measure varies continuously with the dynamics in the L1-norm. We also describe a concrete application.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7976845854f4c0b6855245edb630563ee015c53f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Vilton Pinheiro
- Stefano Luzzatto
- Zemer Kosloff
- A. Korepanov
- Ian Melbourne
- José F. Alves
- Maria José Pacifico
- Marcelo Viana
Citations in the corpus
- Strong statistical stability of non-uniformly expanding maps (2003, background): “Moreover, the assumption on the constants β andρ as in condition (U3) of [5] is trivially satisfied.”
- Markov structures and decay of correlations for non-uniformly expanding dynamical systems☆ (2002, methodology): “the density of the SRB measure varies continuously in the L(1) norm with f [5]; 5.”
- Martingale–coboundary decomposition for families of dynamical systems (2016, background): “11 with statistical stability following from [25] and [8] respectively (see the corresponding examples in [37] for details).”