Seminarium Wydziału Fizyki Technicznej i Matematyki Stosowanej
19 lutego 2025 r. (środa) o godz. 11.15 w sali 121 GG, Prof. Stefano Luzzatto z Mathematics Section of Abdus Salam International Centre for Theoretical Physics, Trieste, Italy (https://www.stefanoluzzatto.net/)
wygłosi wykład pt. „Computer Assisted Computations in the Quadratic Family”
Abstract:
It has been known already for 25 years that almost every parameter in the one-dimensional quadratic family is either “regular” (has an attracting periodic orbit) or “stochastic” (has an invariant probability measure absolutely continuous with respect to Lebesgue and with positive Lyapunov exponent). Interestingly, the set of regular and stochastic parameters have very different topological structures: the set of regular parameters is open and dense in the parameter space, and therefore the set of stochastic parameters is nowhere dense. However, both of them have positive Lebesgue measure.
Very little is known about the actual value of the measure of the two sets, and for 90% of parameters it is not known if they are regular or stochastic. In this talk I will explain more in detail the problem and discuss some work in progress which uses rigorous numerics and computer-assisted computations to address this question.