Law of iterated logarithm and invariance principle for one-parameter families of interval maps

Daniel Schnellmann (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This result will follow from an almost sure invariance principle for the Birkhoff sum, as a function on the parameter space. Furthermore, we obtain a similar result for general one-parameter families of piecewise expanding maps on the interval.

Mots clés: Almost sure invariance principle; Law of iterated logarithm; One-parameter families; Interval maps; Transversality; Tent maps

Domaines: Systèmes dynamiques [math.DS]; Probabilités [math.PR]

Daniel Schnellmann. Law of iterated logarithm and invariance principle for one-parameter families of interval maps. 2013. ⟨hal-00861987⟩