CRM: Centro De Giorgi
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Regular and Stochastic Behaviour in Dynamical Systems

A parameter almost sure invariance principle (ASIP) for the quadratic family

speaker: Viviane Baladi (CNRS and ITS-ETHZ)

abstract: After recalling what is an ASIP and how it can appear in dynamics, we will discuss and motivate the following joint result with Magnus Aspenberg and Tomas Persson: Consider the quadratic family Ta(x) = a x (1 - x), for x in 0, 1 and parameters a in (2,4). For any

transversal Misiurewicz parameter b, we find a positive measure subset Omega of mixing Collet- Eckmann parameters such that for any Holder function f with nonvanishing autocorrelation for b, the

functions fa(Ta{k}(12)) (where fa is a suitable normalisation of f) for the normalised Lebesgue measure on a positive measure subset of Omega (depending on f) satisfy an ASIP.

Mon 5 Jun, 10:00 - 11:00, Aula Dini
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