Growth of normalizing sequences in limit theorems for conservative maps

2018/03/30 by Gouëzel, Sébastien
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.11472

Abstract

We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an additional slowly varying factor. We show that, ingeneral, there can be no nondegenerate limit theorem with a normalizingsequence that grows exponentially, but that there are examples where itgrows like a stretched exponential, with an exponent arbitrarily close to 1.

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