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Matteo Tanzi: Self-sustaining measures for high-dimensional weakly coupled maps

Time: Thu 2022-03-10 13.00

Location: Room 3721, Lindstedtsvägen 25

Participating: Matteo Tanzi (NYU)

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Abstract: In this talk, I will first review some recent results on self-consistent transfer operators which are nonlinear operators describing the time evolution of weakly coupled maps in the thermodynamic limit where the number of coupled maps goes to infinity. In particular, I will focus on results concerning existence of fixed states, their stability, and persistence under perturbations. Then I will show how to use self-consistent operators to describe the evolution of measures for weakly coupled maps where the number of coupled maps is very large, but finite, leading to the definition of self-sustaining measures. These are “almost” invariant measures for the dynamic, and although they might be very different from the asymptotic equilibrium states of the system, they describe its statistical behavior for stretches of time that are exponentially large in the number of coupled maps.