## Topological Measurements of Invariant Sets in Discrete Dynamical SystemsCoarse, topological measurements of dynamical systems defined
by maps can be used to uncover information about invariant sets for the
system. These techniques are based on the Conley index and have
been used to detect invariant structures from fixed points and periodic
orbits, to connecting orbits and sets which exhibit chaotic symbolic
dynamics. More notably, these techniques have been used to study
both finite-dimensional and infinite-dimensional systems and to prove
the existence of unstable invariant sets. The method relies on first
building a pair of compact sets called an |

Towards automated chaos verification

Proc. Equadiff 2003, World Scientific, Singapore, 157--162, 2005.

S. Day, O. Junge, K. Mischaikow

http://www.math.wm.edu/~sday/henon_comp.html

A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems

SIAM Journal on Applied Dynamical Systems, 3 (2004), no. 2, 117--160.

S. Day, O. Junge, K. Mischaikow

http://www.math.kyoto-u.ac.jp/~arai/