Self-sustaining measures for high-dimensional coupled maps with and without noise

Abstract: I will describe the evolution of measures for coupled dynamical systems with/without noise where the number of coupled units is large, but finite. I will compare the evolution for the finite dimensional system with its thermodynamic limit, which is described by a nonlinear self-consistent transfer operator. In particular, I will give sufficient conditions for the equilibrium states of the thermodynamic limit to be “self-sustaining” for the finite dimensional system: These states are characterized by being “almost” invariant for the finite system, and although might be far from any stationary state, they describe the statistical behavior of the system for long transients whose duration scales exponentially with the number of coupled units.

WEB SITE:  http://www.crm.sns.it/course/6317/

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