Dynamical systems, ergodic theory and observation spaces
Suddhasattwa Das
Abstract:
This is the introductory part of the two part talk, aimed for a general
audience. Dynamical systems, both continuous and discrete-time are present
in many physical systems and are implicitly studied in many mathematical
settings. These talks will be about the "operator theoretic" approach to
dynamical systems, which has numerous applications, both theoretical and
application based. We will introduce basic concepts like flows, invariant
measures, ergodicity, ergodic convergence, followed by L2 spaces and kernel
integral operators. The concept of Koopman operators and their spectrum
will also be introduced, setting the stage for Talk 2, were the author's
results will be presented.