Phase transitions in a piecewise expanding coupled map lattice with linear nearest neighbour coupling

Nonlinearity

Volumn 19, Issue 9, 2006, Pages 2193-2210

  Bardet, Jean Baptiste ^a   Keller, Gerhard ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747394116     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/19/9/012     Document Type: Article

References (29)

1. Baladi V 2000 Positive transfer operators and decay of correlations (Advanced Series in Nonlinear Dynamics vol 16) (Singapore: World Scientific)
2. Baladi V, Degli Eposti M, Isola S, Järvenpää E and Kupiainen A 1998 The spectrum of weakly coupled map lattices J. Math. Pures Appl. 77 539-84
3. Bardet J-B 2002 Limit theorems for coupled analytic maps Probab. Theory Relat. Fields 124 151-77
4. Blank M and Bunimovich L 2003 Multicomponent dynamical systems: SRB measures and phase transitions Nonlinearity 16 387-401
5. Boldrighini C, Bunimovich L A, Cosimi G, Frigio S and Pellegrinotti A 2001 Ising-type and other transitions in one-dimensional coupled map lattices with sign symmetry J. Stat. Phys. 102 1271-83
6. Bowen R 1977 Bernoulli maps of the unit interval Israel J. Math. 28 161-8
7. Bricmont J and Kupiainen A 1995 Coupled analytic maps Nonlinearity 8 379-96
8. Bricmont J and Kupiainen A 1996 High temperature expansions and dynamical systems Commun. Math. Phys. 178 703-32
9. Bunimovich L A and Sinai Ya G 1988 Space-time chaos in coupled map lattices Nonlinearity 1 491-516
10. Fischer T and Rugh H H 2000 Transfer operators for coupled analytic maps Ergod. Theory Dyn. Syst. 20 109-43
11. Gielis G and MacKay R 2000 Coupled map lattices with phase transitions Nonlinearity 13 867-88
12. Jiang M 2003 Sinai-Ruelle-Bowen measures for lattice dynamical systems J. Stat. Phys. 111 863-902
13. Just W and Schmüser F 2005 On phase transitions in coupled map lattices Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Physics vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 33-64
14. Katok A and Hasselblatt B 1995 Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications vol 54) (Cambridge: Cambridge University Press)
15. Keller G 1997 Mixing for finite systems of coupled tent maps Proc. Steklov Inst. Math. vol 216 pp 315-21 (also: Erwin-Schrödinger-Institut Preprint ftp://ftp.esi.ac.at/pub/Preprints/esi388.pdf"ftp://ftp.esi.ac.at/pub/ Preprints/esi388.pdf" ftp://ftp.esi.ac.at/pub/Preprints/esi388.pdf
16. Keller G 2000 An ergodic theoretic approach to mean field coupled maps Fractal Geometry and Stochastics II (Progress in Probability vol 46) ed C Bandt et al (Basle: Birkhäuser) pp 183-208
17. Keller G and Künzle M 1992 Transfer operators for coupled map lattices Ergod. Theory Dyn. Syst. 12 297-318
18. Keller G and Liverani C 1999 Stability of the spectrum for transfer operators Ann. della Scuola Norm. Super. di Pisa, Sci. fis. Mat. XXVIII 141-52
19. Keller G and Liverani C 2004 Coupled map lattices without cluster expansion Discrete Contin. Dyn. Syst. 11 325-35
20. Keller G and Liverani C 2005 A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Physics vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 115-51
21. Keller G and Liverani C 2006 Uniqueness of the SRB measure for piecewise expanding weakly coupled map lattices in any dimension Commun. Math. Phys. 262 33-50
22. Keller G and Rugh H H 2004 Eigenfunctions for smooth expanding circle maps Nonlinearity 17 1723-30
23. Keller G and Zweimüller R 2002 Unidirectionally coupled interval maps: between dynamics and statistical mechanics Nonlinearity 15 1-24
24. Lebowitz J L, Maes C and Speer E R 1990 Statistical mechanics of probabilistic cellular automata J. Stat. Phys. 59 117-70
25. MacKay R 2005 Incecomposable coupled map lattices with non-unique phase Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems (Lecture Notes in Physics vol 671) ed J-R Chazottes and B Fernandez (Berlin: Springer) pp 65-94
26. Miller J and Huse D A 1993 Macroscopic equilibrium from microscopic irreversibility in chaotic coupled map lattices Phys. Rev. E 48 2528-35
27. Rugh H H 2002 Coupled maps and analytic function spaces Ann. Sci. cole Norm. Sup. 35 489-535
28. Rychlik M 1983 Bounded variation and invariant measures Studia Math. LXXVI 69-80
29. Toom A L 1980 Stable and attractive trajectories in multicomponent systems Multicomponent Random Systems ed R L Dobrushin and Ya G Sinai (New York: Dekker)