Coupled map lattices with asynchronous updatings
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 421-479. 
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     author = {Fischer, Torsten},
     title = {Coupled map lattices with asynchronous updatings},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {421--479},
     publisher = {Elsevier},
     volume = {37},
     number = {4},
     year = {2001},
     mrnumber = {1876839},
     zbl = {0981.37016},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2001__37_4_421_0/}
}
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Fischer, Torsten. Coupled map lattices with asynchronous updatings. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 4, pp. 421-479. http://www.numdam.org/item/AIHPB_2001__37_4_421_0/

[1] L Arnold, Random Dynamical Systems, Springer, 1998. | MR

[2] V Baladi, M Degli Esposti, S Isola, E Järvenpää, A Kupiainen, The spectrum of weakly coupled map lattices, J. Math. Pures et Appl. 77 (1998) 539-584. | MR | Zbl

[3] H Bauer, Wahrscheinlichkeitstheorie, de Gruyter, 1991. | MR | Zbl

[4] J Bricmont, A Kupiainen, Coupled analytic maps, Nonlinearity 8 (1995) 379-396. | MR | Zbl

[5] J Bricmont, A Kupiainen, High temperature expansions and dynamical systems, Comm. Math. Phys. 178 (1996) 703-732. | MR | Zbl

[6] J Bricmont, A Kupiainen, Infinite dimensional SRB-measures. Lattice dynamics (Paris, 1995), Physica D 103 (1997) 1-4, 18-33. | MR

[7] L.A Bunimovich, Coupled map lattices: One step forward and two steps back, Physica D 86 (1995) 248-255. | MR | Zbl

[8] L.A Bunimovich, Y.G Sinai, Space-time chaos in coupled map lattices, Nonlinearity 1 (1988) 491-516. | MR | Zbl

[9] R.L Dobrushin, 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. | MR

[10] R.L Dobrushin, 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 (Eds.), Multicomponent Random Systems, Advances in Probability and Related Topics, 6, 1980, (originally published in Russian). | MR | Zbl

[12] T Fischer, Transfer operators for deterministic and stochastic coupled map lattices, Thesis, University of Warwick, 1998.

[13] T Fischer, H.H Rugh, Transfer operators for coupled analytic maps, Ergodic Theory Dynamical Systems 20 (2000) 109-143. | MR | Zbl

[14] R.J Glauber, Time-dependent statistics of the Ising model, J. Math. Phys. 4 (1963) 294-307. | MR | Zbl

[15] T.E Harris, Nearest-neighbor Markov interaction processes on multidimensional lattices, Adv. Math. 9 (1972) 66-89. | MR | Zbl

[16] R Holley, A class of interactions in an infinite particle system, Adv. Math. 5 (1970) 291-309. | MR | Zbl

[17] M Jiang, Equilibrium states for lattice models of hyperbolic type, Nonlinearity 8 (5) (1994) 631-659. | MR | Zbl

[18] M Jiang, Ergodic properties of coupled map lattices of hyperbolic type, Penns. State University Dissertation, 1995.

[19] M Jiang, A Mazel, uniqueness of Gibbs states and exponential decay of correlation for some lattice models, J. Statist. Phys. 82 (3-4) (1995). | MR

[20] M Jiang, Ya.B Pesin, Equilibrium measures for coupled map lattices: existence, uniqueness and finite-dimensional approximations, CMP 193 (1998) 675-711. | MR | Zbl

[21] G Keller, M Künzle, Transfer operators for coupled map lattices, Ergodic Theory Dynamical Systems 12 (1992) 297-318. | MR | Zbl

[22] S Lang, Real and Functional Analysis, Springer, 1993. | MR | Zbl

[23] T.M Liggett, Existence theorems for infinite particle systems, Trans. Amer. Math. Soc. 165 (1972) 471-481. | MR | Zbl

[24] T.M Liggett, Interacting Particle Systems, Grundlehren der mathematischen Wissenschaften, 276, Springer, 1985. | MR | Zbl

[25] C Maes, A Van Moffaert, Stochastic stability of weakly coupled lattice maps, Nonlinearity 10 (1997) 715-730. | MR | Zbl

[26] Ya.B Pesin, Ya.G Sinai, Space-time chaos in chains of weakly interacting hyperbolic mappings, Adv. Soviet Math. 3 (1991) 165-198. | MR | Zbl

[27] F Spitzer, Random processes defined through the interaction of an infinite particle system, in: Springer Lecture Notes in Mathematics, 89, Springer, 1969, pp. 201-223. | MR | Zbl

[28] F Spitzer, Interaction of Markov processes, Adv. Math. 5 (1970) 246-290. | MR | Zbl

[29] D.L Volevich, The Sinai-Bowen-Ruelle measure for a multidimensional lattice of interacting hyperbolic mappings, Russ. Akad. Dokl. Math. 47 (1993) 117-121. | MR | Zbl

[30] D.L Volevich, 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. | MR | Zbl