Unidirectionally coupled interval maps: Between dynamics and statistical mechanics

Nonlinearity

Volumn 15, Issue 1, 2002, Pages 1-24

  Keller, Gerhard ^a   Zweimüller, Roland ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041973433     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/1/301     Document Type: Article

References (22)

1. Afraimovich V and Fernandez B 2000 Topological properties of linearly coupled expanding map lattices Nonlinearity 13 973-93
2. Baladi V et al 1998 The spectrum of weakly coupled map lattices J. Math. Pures Appl. 77 539-84
3. Blank M and Keller G 1997 Stochastic stability versus localization in chaotic dynamical systems Nonlinearity 10 81-107
4. Bowen R 1977 Bernoulli maps of the interval Israel J. Math. 28 161-8
5. Boyarsky A and Góra P 1997 Laws of Chaos (Invariant Measures and Dynamical Systems in One Dimension) (Basle: Birkhäuser)
6. Bricmont J and Kupiainen A 1995 Coupled analytic maps Nonlinearity 8 379-96
7. Bricmont J and Kupiainen A 1996 High temperature expansions and dynamical systems Commun. Math. Phys. 178 703-32
8. Bunimovich L A and Sinai Ya G 1998 Spacetime chaos in coupled map lattices Nonlinearity 1 491-516
9. Evans L C and Gariepy R F 1992 Measure Theory and Fine Properties of Functions (Boca Raton, FL: CRC Press)
10. Fischer T and Rugh H H 2000 Transfer operators for coupled analytic maps Ergod. Th. Dynam. Sys. 20 109-43
11. Järvenpää E and Järvenpää M 2001 On the definition of SRB-measures for coupled map lattices Commun. Math. Phys. 220 1-12
12. Jiang M and Pesin Ya 1998 Equilibrium measures for coupled map lattices: existence, uniqueness and finite-dimensional approximations Commun. Math. Phys. 193 675-711
13. Keller G 1982 Stochastic stability in some chaotic dynamical systems Monats. Math. 94 313-33
14. Keller G 1996 Coupled map lattices via transfer operators on functions of bounded variation Stochastic and Spatial Structures of Dynamical Systems vol 45, ed S J van Strien and S M Verduyn Lunel (Kon. Nederl. Akad. Wetensch. Verhandelingen, Afd. Natuurkunde, Eerste Reeks) pp 71-80
15. Keller G 1997 Mixing for finite systems of coupled tent maps Proc. Steklov Inst. Math. 216 315-21.
16. Keller G 2000 An ergodic theoretic approach to mean field coupled interval maps Progress in Probability vol 46 (Basle: Birkhäuser) pp 183-208
17. Keller G 1999 Interval maps with strictly contracting Perron-Frobenius operators Int. J. Bifurc. Chaos 9
18. Keller G and Künzle M 1992 Transfer operators for coupled map lattices Ergod. Th. Dynam. Sys. 12 297-318
19. Keller G and Liverani C 2000 Stability of the spectrum for transfer operators Ann. Mat. Sc. Norm. Pisa 28 141-52.
20. Künzle M 1993 Invariante Maße für gekoppelte Abbildungsgitter Thesis Erlangen
21. Lasota A and Yorke J A 1973 On the existence of invariant measures for piecewise monotonic transformations Trans. Am. Math. Soc. 186 481-8
22. Ziemer W P 1989 Weakly Differentiable Functions (Graduate Texts in Mathematics vol 120) (Berlin: Springer)