Ergodic theory: a statistical description of chaotic dynamical systems

SIAM Student Seminar
Friday, December 3, 2021 - 2:30pm for 1 hour (actually 50 minutes)
Skiles 169
Alex Blumenthal – Georgia Tech
Daniyar Omarov

Dynamical systems model the way that real-world systems evolve in time. While the time-asymptotic behavior of many systems can be characterized by “simple” dynamical features such as equilibria and periodic orbits, some systems evolve in a chaotic, seemingly random way. For such systems it is no longer meaningful to track one trajectory at a time individually- instead, a natural approach is to treat the initial condition as random and to observe how its probabilistic law evolves in time. This is the core idea of ergodic theory, the topic of this talk. I will not assume much beyond some basics of probability theory, e.g., random variables.