The starting point of statistical mechanics is the assumption that deterministic laws of motion can produce "unpredictable random behavior". But how to make sense, measure, or analyze randomness in a setting which is purely deterministic? This is the purpose of ergodic theory.
An important aspect of the theory is that it provides tools for handling dependent stochastic processes under very weak (sometimes optimal) assumptions. This is important, because the time series produced by deterministic dynamical systems usually do not exhibit any form of independence in the standard probabilistic sense -- therefore they are not covered by the classical models of probability theory (Bernoulli processes, Markov processes, Brownian motion etc.)
The course will survey the basic ideas of the theory, including ergodic theorems, some spectral theory, and a thorough introduction to entropy. Other topics will be covered, depending on the background and interests of the class, and the time at hand.
Prerequisites: some background in measure theory will be helpful.
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