arXiv:math/0610969 Abstract

arXiv:math/0610969 [math.DS]Abstract References Reviews Resources

A "metric" complexity for weakly chaotic systems

Published 2006-10-31Version 1

We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its value is given by a sort of local entropy, this indicator is quite simple to be calculated. We give some example of calculation in nontrivial systems (interval exchanges, piecewise isometries e.g.) and a formula similar to the Ruelle-Pesin one, relating the complexity indicator to some initial condition sensitivity indicators playing the role of positive Lyapunov exponents.

Comments: 15 pages, no figures. Article

Categories: math.DS

Subjects: 37A35

Keywords: weakly chaotic systems, complexity indicator, initial condition sensitivity indicators playing, large measure subset, interval exchanges

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