Coupled map lattices with asynchronous updatings

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 37, Issue 4, 2001, Pages 421-479

  Fischer, Torsten ^a  

^a Interdisziplinares Zentrum W   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042238351     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(01)01080-9     Document Type: Article

References (30)

1. Arnold L. Random Dynamical Systems. 1998;Springer.
2. Baladi V., Degli Esposti M., Isola S., Järvenpää E., Kupiainen A. The spectrum of weakly coupled map lattices. J. Math. Pures et Appl. 77:1998;539-584.
3. Bauer H. Wahrscheinlichkeitstheorie. 4th edn. 1991;de Gruyter.
4. Bricmont J., Kupiainen A. Coupled analytic maps. Nonlinearity. 8:1995;379-396.
5. Bricmont J., Kupiainen A. High temperature expansions and dynamical systems. Comm. Math. Phys. 178:1996;703-732.
6. Bricmont J., Kupiainen A. Infinite dimensional SRB-measures. Lattice dynamics (Paris, 1995). Physica D. 103:1997;1-4. 18-33.
7. Bunimovich L.A. Coupled map lattices: One step forward and two steps back. Physica D. 86:1995;248-255.
8. Bunimovich L.A., Sinai Y.G. Space-time chaos in coupled map lattices. Nonlinearity. 1:1988;491-516.
9. Dobrushin R.L. Markov processes with a large number of locally interacting components: existence of a limit process and its ergodicity. Problems Inform. Transmission. 7:1971;149-164.
10. Dobrushin R.L. Markov processes with many locally interacting components - the reversible case and some generalizations. Problems Inform. Transmission. 7:1971;235-241.
11. Dobrushin R.L., Sinai Ya.G. Multicomponent Random Systems. Advances in Probability and Related Topics. 6:1980;. (originally published in Russian).
12. Fischer T. Transfer operators for deterministic and stochastic coupled map lattices, Thesis. 1998;University of Warwick.
13. Fischer T., Rugh H.H. Transfer operators for coupled analytic maps. Ergodic Theory Dynamical Systems. 20:2000;109-143.
14. Glauber R.J. Time-dependent statistics of the Ising model. J. Math. Phys. 4:1963;294-307.
15. Harris T.E. Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. Math. 9:1972;66-89.
16. Holley R. A class of interactions in an infinite particle system. Adv. Math. 5:1970;291-309.
17. Jiang M. Equilibrium states for lattice models of hyperbolic type. Nonlinearity. 8:(5):1994;631-659.
18. Jiang M. Ergodic properties of coupled map lattices of hyperbolic type. 1995;Penns. State University Dissertation.
19. Jiang M., Mazel A. uniqueness of Gibbs states and exponential decay of correlation for some lattice models. J. Statist. Phys. 82:(3-4):1995.
20. Jiang M., Pesin Ya.B. Equilibrium measures for coupled map lattices: existence, uniqueness and finite-dimensional approximations. CMP. 193:1998;675-711.
21. Keller G., Künzle M. Transfer operators for coupled map lattices. Ergodic Theory Dynamical Systems. 12:1992;297-318.
22. Lang S. Real and Functional Analysis. 3rd edn. 1993;Springer.
23. Liggett T.M. Existence theorems for infinite particle systems. Trans. Amer. Math. Soc. 165:1972;471-481.
24. Liggett T.M. Interacting Particle Systems. Grundlehren der mathematischen Wissenschaften. 276:1985;Springer.
25. Maes C., Van Moffaert A. Stochastic stability of weakly coupled lattice maps. Nonlinearity. 10:1997;715-730.
26. Pesin Ya.B., Sinai Ya.G. Space-time chaos in chains of weakly interacting hyperbolic mappings. Adv. Soviet Math. 3:1991;165-198.
27. Spitzer F. Random processes defined through the interaction of an infinite particle system. Springer Lecture Notes in Mathematics. 89:1969;201-223 Springer.
28. Spitzer F. Interaction of Markov processes. Adv. Math. 5:1970;246-290.
29. Volevich D.L. The Sinai-Bowen-Ruelle measure for a multidimensional lattice of interacting hyperbolic mappings. Russ. Akad. Dokl. Math. 47:1993;117-121.
30. Volevich D.L. Construction of an analogue of Bowen-Ruell-Sinai measure for a multidimensional lattice of interacting hyperbolic mappings. Russ. Akad. Math. Sbornik. 79:1994;347-363.