Multicomponent dynamical systems: SRB measures and phase transitions

Nonlinearity

Volumn 16, Issue 1, 2003, Pages 387-401

  Blank, Michael ^a,b   Bunimovich, Leonid ^b  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242276319     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/1/322     Document Type: Review

References (20)

1. Blank M L 2001 Stability and Localization in Chaotic Dynamics (Moscow: MCCME)
2. Blank M L 1997 Generalized phase transitions in finite coupled map lattices Physica D 103 34-50
3. Bricmont J and Kupiainen A 1996 High temperature expansions and dynamical systems Commun. Math. Phys. 178 703-32
4. Bunimovish L A and Carlen E A 1995 On the problem of stability in lattice dynamical systems J. Diff. Eqns 123 213-19
5. Bunimovich L A and Sinai Ya G 1988 Spacetime chaos in coupled map lattices Nonlinearity 1 491-516
6. van Enter A C D, Fernandez R and Sokal A D 1995 Regularity properties and pathologies of position-space renormalization group transformation: scope and limitation of Gibbsian theory J. Stat Phys. 72 679-1167
7. Farmer D J, Ott E and Yorks J A 1983 The dimension of chaotic attractors Physica D 7 153-80
8. Gielis G and MacKay R S 2000 Coupled map lattices with phase transitions Nonlinearity 13 867-88
9. Goldstein S, Kuik J, Lebowitz J L and Maes C 1989 From PCA's to equilibrium measures and back Commun. Math. Phys. 125 71-9
10. Goldstein S, Kuik J and Schlijper A G 1990 Entropy and global Markov properties Commun. Math. Phys. 126 469-82
11. Hu H and Young L-S 1995 Nonexistence of SBR measures for some diffeomorphisms which are 'almost Anosov' Erg. Th. Dyn. Sys. 15 67-76
12. Inoue T 2000 Sojourn times in small neighborhoods of indifferent fixed points of one-dimensional dynamical systems Erg. Th. Dyn. Sys. 20 241-58
13. Kaneko K 1990 Globally coupled chaos violates the law of large numbers Phys. Rev. Lett. 65 1-4
14. Keller G 2001 Completely mixing maps without limit measure Preprint
15. Lebowitz J L, Maes C and Speer E 1990 Statistical mechanics of probabilistics cellular automata J. Stat. Phys. 59 117-70
16. Misiurewicz M and Zdunik A 1985 Convergence of images of certain measures Statistical Physics and Dynamical Systems (Koszeg, 1984) ed J Fritz, A Jaffe and D Szacz Progr. Phys. vol 10 (Boston, MA: Birkhauser) pp 203-19
17. van Strien S and Verdun S M (ed) 1996 Stochastic and Spatial Structure of Dynamical Systems (Amsterdam: North-Holland)
18. 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)
19. Ulam S 1960 Problems in Modern Mathematics (New York: Interscience)
20. Young L-S 2002 What are SBR measures, and which dynamical systems have them J. Stat. Phys. 108 733-54