DSNT Seminar: A parameter almost sure invariance principle (ASIP) for the quadratic family
- Date: 8 September 2023, 10:15–11:15
- Location: Ångström Laboratory, Å64119
- Type: Seminar
- Lecturer: Viviane Baladi
- Organiser: Matematiska institutionen
- Contact person: Reza Mohammadpour
Viviane Baladi from CNRS (The National Centre for Scientific Research, France) holds this seminar. Welcome to participate!
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 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.
This is a seminar in our seminar series on Dynamical Systems and Number Theory (DSNT).