Selfconsistent Transfer Operators: Existence and stability of fixed points in presence of strong coupling
speaker: Matteo Tanzi (King's College)abstract: Selfconsistent transfer operators (STOs) are nonlinear operators describing the thermodynamic limit of mean-field coupled maps, and are the discrete time analogues of McKean-Vlasov equations. They allow to model and study the emergent behaviour of interacting chaotic units in discrete time and, more generally, of systems whose evolution is not Hamiltonian or for which there are no evident conserved quantities.
The study of the dynamics of STOs gives information on the emergent behaviour in the thermodynamic limit and, in particular, on the existence and stability of equilibrium measures. Studies of STOs have mostly been limited to the case of small coupling where the STO is close to a linear operator. In this talk, I will describe recent results providing sufficient conditions for the existence and stability of fixed points in the strong coupling regime where the STO presents “genuinely” nonlinear dynamics with bounded basins of attraction and multiple fixed points.
timetable:
Thu 12 Sep, 14:30 - 15:05, Aula Dini
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