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We perform computer simulations of some one-dimensional models of coupled map lattices (CML) with symmetry and diffusive nearest neighbour coupling, to study Ising-type transitions. Such transitions appear to be related to the presence of a dip (minimum) in the plot of the Lyapunov dimension versus coupling parameter.
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Tom
Strony
5--17
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
- Dipartimento cli Matematica, Universita di Roma La Sapienza, P. A. Morn 2. 00187, Roma, Italy
autor
- Dipartimento di Matematica e Fisica, Universita ili Camerino Via Madonna delle Careeri, 62022 Camerino, Italy
autor
- Dipartimento di Matematica e Fisica, Universita ili Camerino Via Madonna delle Careeri, 62022 Camerino, Italy
autor
- Dipartimento di Matematica.Universita degli Studi di Roma Tre, Largo San Leonardo Maria Ido 1,00146 Roma, Italy
Bibliografia
- [1] Monin A. S., Yaglom A.M., Statistical Fluid Mechanics, Mechanics of Turbulence, MIT Press, Cambridge, Mass., 1971
- [2] Batchelor K. G.,An Introduction to Fluid Dynamics, Cambridge University Press, 1967
- [3] Whither Turbulence , Lecture Notes in Physics, Springer 1990
- [4] Joseph D. D., Stability of Fluid Motions Vol. I and II, Springer Tracts in Natural Philosophy Vol. 28, Springer-Verlag, 1976
- [5] Theory and Applications of coupled Map Lattices ed. by K.Kaneko, John Wiley & Sons, 1993
- [6] Bunimovich L. A., Sinai Ya. G., Spacetime Chaos in coupled Map Lattices, Nonlinearity 1,491-516,1988
- [7] Bunimovich L. A., Sinai Ya. G. in [5]
- [8] Sinai Ya. G., Gibbs Measures in Ergodic Theory, Russian Mathem. Surveys 27, 21-64, 1972
- [9] Ruelle D., Thermodynamic Formalism, Addison-Wesley, London, 1978
- [10] Bunimovich L. A., Lambert A., Lima R., The Emergence of coherent Structures in coupled Map Lattices, Journal of Statistical Physics61, Nos. 1/2, 253-262, 1990
- [11] Rakhmanov A. I., Rakhmanova N. K., On one dynamic System with discrete Time, Preprint of the Keldysh.Inst, for Appl.Math., Moscow, 1990
- [12] Giberti C., Vemia C., On the Presence of normally attracting Manifolds containing periodic or quasi periodic Orbits in coupled Map Lattices, Int. J. Bifurcation and Chaos 3,1503-1514,1993
- [13] Giberti C., Vemia C., Normally attracting Manifolds and periodic Behaviour in 1-D and 2-D coupled Map Lattices, Chaos 4,651 -663, 1994
- [14] Grassbcrgcr P., Schreiber T., Phase Transitions in coupled Map Lattices, Physica I) 50, 177-186,1991
- [15] Afraimovich V., Bunimovich L.A., Simplest Structures in coupled Map Lattices and their Stability, Random and Computational Dynamics 1.423-444, 1993
- [16] Bunimovich L. A. , Carlen E. A., On the Problem of Stability in Lattice dynamical Systems, J,Differential Equations 123,213-229, 1995
- [17] Miller J., Huse D., Macroscopic Equilibrium from microscopic Irreversibility in a chaotic coupled-map Lattice, Phys. Rev. E 48, 2528-2535, 1993
- [18] Boldrighini C., Bunimovich L, A., Cosimi G., Frigio S., Pcllcgrinotti A.. /sing-type transitions in coupled map lattices. Journal Stat.Phys Vol.80 N.5/6 11 85-1205, 1995
- [19] Bcncttin G„ Galgani L., Giorgilli A., Strclcyn J. M., Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them.Part I .theory., Mcccanica 15,9-20, 1980
- [20] Bcncttin G„ Galgani L., Giorgilli A,, Strclcyn J. M„ Lyapunov charcteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing till of them.Part 2:numerical applications., Meccanica 15,21-30, 1980
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Bibliografia
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bwmeta1.element.baztech-article-BAT3-0019-0001