A "metric" complexity for weakly chaotic systems

Details A "metric" complexity for weakly chaotic systems A "metric" complexity for weakly chaotic systems

2006-10-31

arxiv.org/abs/math/0610969v1

Mathematics

Dynamical Systems

15 pages, no figures. Article

Scientific paper

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.

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