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.