The Erwin Schrr Odinger International Institute for Mathematical Physics Boltzmann's Ergodic Hypothesis, a Conjecture for Centuries?

An overview of the history of Ludwig Boltzmann’s more than one hundred year old ergodic hypothesis is given. The existing main results, the majority of which is connected with the theory of billiards, are surveyed, and some perspectives of the theory and interesting and realistic problems are also mentioned.

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