SMRI Seminar: Tanzi -- Coupled Chaotic Maps and Self-Consistent Transfer Operators

Abstract: At the end of the 1980s, globally coupled maps (GCMs) emerged as
high-dimensional models for complex systems.  These models feature simple equations
where several variables are coupled symmetrically all-to-all, and display a rich variety
of behaviors, including synchronization, phase ordering, and turbulence.  Rigorous
mathematical studies of the dynamics of GCMs have primarily focused on their mean-field
limit—that is, the behavior of the system’s average state as the number of maps
approaches infinity.  This limit is governed by a nonlinear operator known as the
self-consistent transfer operator, which dictates the evolution of the mean field.  In
this talk, I will provide a brief overview of the origin of the study of self-consistent
transfer operators and discuss some recent progress in the field focusing on coupled
chaotic maps.