Applied Maths Seminar: Tanzi -- Selfconsistent Transfer Operators: Existence and stability of fixed points in presence of strong coupling

Matteo Tanzi (King's College, London) is visiting until 21st March, and will be giving a
talk in the applied maths seminar entitled "Selfconsistent Transfer Operators: Existence
and stability of fixed points in presence of strong coupling".  

The talk will take place in Carslaw 173 on Wednesday Week 3 at 11am.  We will go to
lunch after the event (free for students).  

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.