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Statistical stability for robust classes of maps with non-uniform expansion

Published online by Cambridge University Press:  09 January 2002

JOSÉ F. ALVES  and
MARCELO VIANA
JOSÉ F. ALVES
Affiliation:
Centro de Matemática da Universidade do Porto, Praça Gomes Teixeira, 4099-002 Porto Portugal (e-mail: jfalves@fc.up.pt)
MARCELO VIANA
Affiliation:
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil (e-mail: viana@impa.br)
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 1 , February 2002 , pp. 1 - 32
Copyright
2002 Cambridge University Press

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