Mathematical Aspects of Chaos
Keywords:
chaos, algorithm, matroidAbstract
We study the pattern recognition algorithms of combinatorial chaos (chaotic). First chaotic introduced in [1]. There are the most universal mathematical construction of chaos and, contrary to all the others, expand the notion of chaos even to finite structures. We give a mathematically exact characterization of chaos in finite sets. For example, a class of chaotic, that is “whirligig” and corresponds to granular chaotic structures, is proposed. The examples of recognition of minimum by the amount of elements among all the others (whirligig, anthill, disorder and quasimatroid etc) are given.
References
Gritsak-Groener V. V., Gritsak-Groener J. Arts Combinatoria. — Academic Press, 2003.
Gritsak-Groener V. V., Gritsak-Groener J. Arts Combinatoria. Vol. 2. — Academic Press, 2006.
Lam L. Introduction to Nonlinear Physics. — Springer, 1997.
Gritsak-Groener V. V., Gritsak-Groener J. Pattern Recognition Algorithms in Statistical Physics. // The Pro-ceedings of the XX-th IUPAP International Conference on Statistical Physics (STATPHYS"20). — Paris, 1998.
Gritsak-Groener V. V. Logic and Categorical Theory for Natural Science. — HRIT Press, N. Y., 1995.
Gritsak-Groener V. V. A Theory of Finite Chaotic. — SLU, 1997.
