Ergodic Theory

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions onMeasure Spaces. The Group is most commonly N,R, R+, and Z.

Ergodic theory had its origins in the work of Boltzmann in statistical mechanics. Its mathematical origins aredue to von Neumann, Birkhoff, and Koopman in the 1930s. It has since grown to be a hugesubject and has applications not only to statistical mechanics, but also to number theory, differential geometry,functional analysis, etc. There are also many internal problems (e.g., ergodic theory being applied to ergodic theory)which are interesting.

References

Billingsley, P. Ergodic Theory and Information. New York: Wiley, 1965.

Cornfeld, I.; Fomin, S.; and Sinai, Ya. G. Ergodic Theory. New York: Springer-Verlag, 1982.

Katok, A. and Hasselblatt, B. An Introduction to the Modern Theory of Dynamical Systems. Cambridge, England: Cambridge University Press, 1996.

Nadkarni, M. G. Basic Ergodic Theory. India: Hindustan Book Agency, 1995.

Parry, W. Topics in Ergodic Theory. Cambridge, England: Cambridge University Press, 1982.

Smorodinsky, M. Ergodic Theory, Entropy. Berlin: Springer-Verlag, 1971.

Walters, P. Ergodic Theory: Introductory Lectures. New York: Springer-Verlag, 1975.

• Thurston's Geometrization Conjecture
• Thwaites Conjecture
• Ticktacktoe
• Tic-Tac-Toe
• Tight Closure
• Tightly Embedded
• Tiling
• Tiling Theorem
• Times
• Titanic Prime
• Titchmarsh Theorem
• Tit-for-Tat
• Tits Group
• Toeplitz Matrix
• Togliatti Surface
• Tomography
• Tooth Surface
• Topological Basis
• Topological Completion
• Topological Dimension
• Topological Entropy
• Topological Groupoid
• Topologically Conjugate
• Topologically Transitive
• Topological Manifold