DENSITY OF MEASURE-THEORETIC DIRECTIONAL ENTROPY FOR LATTICE DYNAMICAL SYSTEMS-Reference-Cited by-同舟云学术

DENSITY OF MEASURE-THEORETIC DIRECTIONAL ENTROPY FOR LATTICE DYNAMICAL SYSTEMS

Published:2008-01 Issue:01 Volume:18 Page:161-168
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

COURBAGE M.¹,KAMIŃSKI B.²

Affiliation:

1. Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS et Université Paris 7-Denis Diderot, Case 7020, Tour 24-14, 5ème étage, 75251 Paris Cedex 05, France

2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

The density of the measure-theoretic directional entropy for the lattice dynamical system is introduced and it is shown that for a lattice dynamical transformation commuting with the shift transformation the density coincides with the entropy of the ℤ2-action generated by these two transformations, i.e. it is a constant function with respect to the direction. It is also proved that in the noncommutative case this result fails to be true.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127408020203

Reference13 articles.

1. V. Afraimovich, Progress in Nonlinear Sciences, Mathematical Problems of Nonlinear Dynamics I, eds. L. M. Lehman and L. P. Shilnikov (2002) pp. 9–30.

2. On the density of directional entropy in lattice dynamical systems

3. A mechanism for localised turbulence

4. Spacetime chaos in coupled map lattices

5. Lattice Dynamical Systems

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