A ”metric” Complexity for Weakly Chaotic Systems
نویسنده
چکیده
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.
منابع مشابه
A COMMON FIXED POINT THEOREM FOR SIX WEAKLY COMPATIBLE MAPPINGS IN M-FUZZY METRIC SPACES
In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete M-fuzzy metric spaces.
متن کاملA COMMON FIXED POINT THEOREM FOR $psi$-WEAKLY COMMUTING MAPS IN L-FUZZY METRIC SPACES
In this paper, a common fixed point theorem for $psi$-weakly commuting maps in L-fuzzy metric spaces is proved.
متن کاملGeneralized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces
In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and coincidence point theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.
متن کاملFixed point theorems for weakly contractive mappings on g-Metric spaces and a homotopy result
In this paper, we give some xed point theorems for '-weak contractivetype mappings on complete G-metric space, which was given by Zaed andSims [1]. Also a homotopy result is given.
متن کاملInformation, initial condition sensitivity and dimension in weakly chaotic dynamical systems
We study generalized indicators of sensitivity to initial conditions and orbit complexity in topological dynamical systems. The orbit complexity is a measure of the asymptotic behavior of the information that is necessary to describe the orbit of a given point. The indicator generalizes, in a certain sense, the Brudno’s orbit complexity (which is strongly related to the entropy of the system). ...
متن کامل