By Roberto Livi (auth.), Eric Goles, Servet Martínez (eds.)

ISBN-10: 9048147344

ISBN-13: 9789048147342

ISBN-10: 9401713235

ISBN-13: 9789401713238

This ebook comprises the classes given on the Fourth college on Statistical Physics and Cooperative structures held at Santiago, Chile, from twelfth to sixteenth December 1994. this faculty brings jointly scientists engaged on matters with regards to fresh traits in advanced platforms. a few of these topics take care of dynamical platforms, ergodic concept, mobile automata, symbolic and mathematics dynamics, spatial platforms, huge deviation conception and neural networks. Scientists operating in those topics come from a number of aeras: natural and utilized arithmetic, non linear physics, biology, machine technology, electric engineering and synthetic intelligence. every one contribution is dedicated to 1 or extra of the former topics. normally they're established as surveys, featuring while an unique perspective concerning the subject and exhibiting regularly new effects. The expository textual content of Roberto Livi matters the examine of coupled map lattices (CML) as versions of spatially prolonged dynamical structures. CML is without doubt one of the such a lot used instruments for the research of spatially prolonged structures. The paper emphasizes rigorous effects in regards to the dynamical habit of 1 dimensional CML; i.e. a uniform genuine neighborhood functionality outlined within the period [0,1], interacting with its nearest acquaintances in a one dimensional lattice.

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W. McDonald, C. Grebogi, E. A. Yorke, Physica D17, 125 (1985). , Progr. Theor. Phys. 72, 480 (1984); I. Waller, R. Kapral, Phys. Rev. A30, 2047 (1984); J. P. S. Pikovsky, Izvestija VUZ, RadiJizika 28,308 (1985). A. Huse, Phys. Rev. E48, 2528 (1993). , Y. R. Sreenivasan, A. K. Suri, Phys Rev. Lett. 69 (1993); Y. Du, E. Ott, Physica D67, 387 (1993). , Theory and Applications of Cellular Automata, World Scientific, Singapore (1986). M. cl ABSTRACT. In this note we review some results about the ergodic theory and topological dynamics of one-dimensional cellular automata.

Yorke, Phys. Lett. W. McDonald, C. Grebogi, E. A. Yorke, Physica D17, 125 (1985). , Progr. Theor. Phys. 72, 480 (1984); I. Waller, R. Kapral, Phys. Rev. A30, 2047 (1984); J. P. S. Pikovsky, Izvestija VUZ, RadiJizika 28,308 (1985). A. Huse, Phys. Rev. E48, 2528 (1993). , Y. R. Sreenivasan, A. K. Suri, Phys Rev. Lett. 69 (1993); Y. Du, E. Ott, Physica D67, 387 (1993). , Theory and Applications of Cellular Automata, World Scientific, Singapore (1986). M. cl ABSTRACT. In this note we review some results about the ergodic theory and topological dynamics of one-dimensional cellular automata.

The flow (X, T) is for the projection with respect to the first coordinate. Let J-£ be a T-invariant measure, and B be the Borel sigma-algebra on X. We define jL over the sigma-algebra by: jL( a(i») = B, generated by the family a(i) = {x E Xjx(i) E a}, a E B, J-£( a). A flow (X, T) is a K-system with respect to the invariant measure J-£ if it is bijective and there exists a sigma-algebra A 00 00 i=O i=O ~ B such that where N is the trivial a-algebra of X. 2. Let F : A Z --+ AZ be a surjective cellular automaton.

### Dynamics of Complex Interacting Systems by Roberto Livi (auth.), Eric Goles, Servet Martínez (eds.)

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