Combinatorics and dynamical systems
The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words. Also combinatorial aspects of dynamical systems are studied. Dynamical systems can be defined on combinatorial objects such as graphs - a particular kind of graph dynamical system is a sequential dynamical system.
See also
References
- "From Combinatorics to Dynamical Systems: Journées de Calcul Formel, Strasbourg, March 22-23, 2002", Frédéric Fauvet, Claude Mitschi, Walter de Gruyter, 2003, ISBN 9783110178753
- "Substitutions in Dynamics, Arithmetics, and Combinatorics", N. Pytheas Fogg, Valérie Berthé, Springer, 2002, ISBN 9783540441410
- "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", Vadim A. Kaimanovich, Andrei Lodkin,AMS Bookstore, 2006, ISBN 9780821842089
- "An Introduction to Sequential Dynamical Systems", Henning S. Mortveit, Christian M. Reidys, Springer, 2007, ISBN 9780387306544
- "Generalized integer partitions, tilings of zonotopes and lattices", Matthieu Latapy, chapter in "Formal Power Series and Algebraic Combinatorics: 12th International Conference, FPSAC'00, Moscow, Russia, June 2000, Proceedings", Edited by Daniel Krob, Alexander A. Mikhalev, Springer, 2000, ISBN 9783540672470
- "Applied Combinatorics on Words", M. Lothaire, Cambridge University Press, 2005, ISBN 9780521848022
- "Symbolic Dynamics and Self-similar Groups", Volodymyr Nekrashevych, chapter in "Holomorphic Dynamics and Renormalization: A Volume in Honour of John Milnor's 75th Birthday", John Willard Milnor, Mikhail Lyubich, Michael Yampolsky, AMS Bookstore, 2008, ISBN 9780821842751
- "Aperiodic Order: Dynamical Systems, Combinatorics, and Operators", Michael Baake, David Damanik, Ian Putnam, Boris Solomyak, 2004 report of the Banff International Research Station for Mathematical Innovation and Discovery