|
Abstract:
In 1931, G. D. Birkhoff published the first formal proof of the
Ergodic Theorem, which served to justify, in specific contexts of
Mathematical Physics, the interchange of time and space averages.
Since then, the theorem has played significant roles in probability
theory, harmonic analysis, and number theory. The object of this
lecture is to sketch a "modern" proof of the theorem and to describe
several applications -- in particular, to the theory of continued
fractions.
|