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## Fractal Dimensions Poincare Recurr by Valentin Afraimovich

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## Afraĭmovich, V. S. (Valentin Senderovich)

Sort order. David Keirsey rated it liked it Sep 16, Huyichen marked it as to-read Apr 19, Kemal Ilter added it Apr 23, Darren Mitton marked it as to-read Oct 23, University of Nijni Novgorod Press, , 9— Chaos 7 , pp. Afraimovich, S.

Afraimovich and G. Afraimovich, G. Afraimovich and L. USSR Sbornik , 5 , , 73— Badii and A. Barreira, A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems, Ergod. Theory and Dyn.

Benkadda and G. Zaslavsky Eds. Blanchard, B.

Host, A. Maass, Topological complexity, Ergod. Theory Dyn. Boffetta, M. Falcione and A. Vulpiani, Predictability: A way to characterize complexity , Phys.

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## Recurrence Quantification of Fractal Structures

Bourbaki, Elements of mathematics. General topology. Part 1. Hermann, Paris, Bowen, Topological entropy for non-compact sets, Trans. Bowen, Hausdorff dimension of quasi-circles. IHES , 50 , — Bohr and D. Rand, Entropy function for characteristic exponents, Physica 25D , — Bruin, Dimensions of recurrence times and minimal subshifts, in: Dynamical systems: from crystal to chaos , J.

- Laminations and Foliations in Dynamics, Geometry and Topology: Proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and ... at Stony Brook.
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- Fractal Dimensions for Poincare Recurrences, Volume 2.
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Gambaudo, P. Save to Library. Beyond Periodicity for Piecewise Contracting Maps more. Publication Date: La Proposicion De Godel more.

### Introduction

Necessary and sufficient conditions are given for master—slave synchronization of any pair of unidirectionally coupled one—dimensional affine cellular automata of rank one. In each case the synchronization condition is expressed in terms In each case the synchronization condition is expressed in terms of the coupling and the arithmetic properties of the automaton local rule. The asymptotic behavior of finite length affine automata of rank one, subjected to Dirichlet boundary conditions, is shown to be equivalent to the synchronization problem.

On the asymptotic properties of piecewise contracting maps more. Ugalde and Pierre Guiraud.

### Correction

Dynamical Systems. We prove the variational principle for dimensions for Poincare recurrences, in the case of invariant sets of dynamical systems with continuous time. To achieve this goal we show that these dimensions can be expressed as roots of a To achieve this goal we show that these dimensions can be expressed as roots of a non-homogeneous Bowen equation. View on ifisica. On the zero-temperature limit of one-dimensional Gibbs measures more. This paper has been withdrawn by the authors due to an error in the main theorem. Dynamic System and Gibbs Measure.

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View on arxiv. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly. We use this technique to estimate the complexity function for genomes of several organisms under the assumption that a genome is a sequence produced by a unknown dynamical system. It is also found that the species which are phylogenetically close each other have similar complexity functions calculated from a sample of their corresponding coding regions.

On the growth of directed complex networks with preferential attachment: Effect upon the prohibition of multiple links more. For example, in a paper citation network a paper does not cite two identical references, and in a network of friends there exists only a single link between two For example, in a paper citation network a paper does not cite two identical references, and in a network of friends there exists only a single link between two individuals. This suggest that the growth and evolution models of complex networks should take into account such feature in order to approximate the topological properties of this class of networks.

The aim of this paper is to propose a growth model of directed complex networks that takes into account the prohibition of the existence multiple links. It is shown through numerical experiments that when multiple links are forbidden, the exponent of the in-degree connectivity distribution,takes values ranging from 1 to infinity. In particular, the proposed multi-link free MLF model is able to predict exponents occurring in real-world complex networks, which range from 1. As an example, the MLF reproduces some topological properties exhibited by the network of fights between airports of the world NFAW ; i.

Mathematical Sciences and Physical sciences. Pointwise dimension and local rates Introduction The theorem Fractal Dimension.