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Statistical stability for robust classes of maps with non-uniform expansion
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2002
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Infinite Dimensional AnalysisEngineeringRobust StatisticInvariant MeasuresSrb MeasureTopological DynamicStatistical StabilityRandom MappingGeneral Uniformity ConditionsNumerical StabilityGlobal AnalysisStochastic GeometryFunctional AnalysisApproximation TheoryStatisticsQuasiconformal MappingOpen SetsStability
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.