The Manneville map : topological , metric and algorithmic entropy Claudio Bonanno
نویسنده
چکیده
We study the Manneville map f(x) = x + x(mod 1), with z > 1, from a computational point of view, studying the behaviour of the Algorithmic Information Content. In particular, we consider a family of piecewise linear maps that gives examples of algorithmic behaviour ranging from the fully to the mildly chaotic, and show that the Manneville map is a member of this family.
منابع مشابه
Fe b 20 02 The Manneville map : topological , metric and algorithmic entropy
We study the Manneville map f(x) = x + x(mod 1), with z > 1, from a computational point of view, studying the behaviour of the Algorithmic Information Content. In particular, we consider a family of piecewise linear maps that gives examples of algorithmic behaviour ranging from the fully to the mildly chaotic, and show that the Manneville map is a member of this family.
متن کاملAlgorithmic information for intermittent systems with an indifferent fixed point
Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the information increases less than linearly with respect to time. We consider two classes of maps of the interval with an indifferent fixed point at the origin and an ...
متن کامل2 5 Se p 20 06 COMPLEXITY FOR EXTENDED DYNAMICAL SYSTEMS
We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, ǫ-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to introduce, for extended dynamical systems, a notion of complexity per unit time and volume which plays the same r...
متن کاملEntropy of a semigroup of maps from a set-valued view
In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...
متن کاملA Thermodynamic Definition of Topological Pressure for Non-compact Sets
We give a new definition of topological pressure for arbitrary (noncompact, non-invariant) Borel subsets of metric spaces. This new quantity is defined via a suitable variational principle, leading to an alternative definition of an equilibrium state. We study the properties of this new quantity and compare it with existing notions of topological pressure. We are particularly interested in the ...
متن کامل