Dear Colleagues, We would like to invite you to the following SPASS <https://sites.google.com/unipi.it/spass> seminar, jointly organized by UniPi, SNS, UniFi and UniSi: *Ergodicity, Positive Lyapunov Exponents, and Partial Damping for Random Switching* by *Jonathan Mattingly* (Duke University) The seminar will take place *tomorrow TUE, 04.07.2023* at *14:00 CET* in Aula Seminari, Department of Mathematics, University of Pisa and streamed online here <https://meet.google.com/gji-phwo-vbg>. The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass --------------------------------------- *Abstract: I will consider some new models inspired by the PDEs/SPDE with complex dynamics such as the 2D Euler and Navier-Stokes equations. The models introduce randomness onto the system through a random splitting scheme. I will explain how the randomly split Galerkin approximations of the 2D Euler equations and other related dynamics can be shown to possess a unique invariant measure that is absolutely continuous with respect to the natural Liouville measure, despite the existence of other invariant measures corresponding to fix points of the PDEs. I will then explain how on proves that the dynamics with respect to this measure has positive Lyapunov exponents almost surely.Lastly, I will discuss recent results which show that the system has a unique invariant measure even when damping is applied to part of the system.This is joint work with Omar Melikechi, Andrea Agazzi, and David Herzog.*