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

Vortrag von Prof. Dr. Viviane Baladi

Datum: 15.05.23  Zeit: 13.30 - 14.30  Raum: ETH HG G 43

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 \(T_a(x) = a x (1 - x)\), 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 \(f_a(T_a^{k}(1/2))\) (where \(f_a\) is a suitable normalisation of \(f\)) for the normalised Lebesgue measure on a positive measure subset of Omega (depending on \(f\)) satisfy an ASIP.