Route to chaotic synchronisation in coupled map lattices: Rigorous results

Discrete and Continuous Dynamical Systems - Series B

Volumn 4, Issue 2, 2004, Pages 435-455

  Fernandez, B ^a   Guiraud, P ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1042279420     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2004.4.435     Document Type: Article

References (18)

1. V. Afraimovich, J-R. Chazottes and A. Cordonet, Synchronization in directionally coupled systems: some rigorous results, Discrete Contin. Dynam. Sys. Ser. B 1 (2001) 421-442.
2. V. Afraimovich and B. Fernandez, Topological properties of linearly coupled expanding map lattices, Nonlinearity 13 (2000) 973-993.
3. P. Ashwin, J. Buescu, and I. Stewart, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity 9 (1996) 703-737.
4. L. Bunimovich, Coupled map lattices: some topological and ergodic properties, Physica D 103 (1997) 1-17.
5. C. Boldrighini, L. Bunimovich, G. Cosimi, S. Frigio and A. Pellegrinotti, Ising-type and other transitions in one-dimensional coupled map lattices with sign symmetry. J. Statist. Phys. 102 (2001), 1271-1283.
6. J. Bricmont and A. Kupiainen, Infinite-dimensional SRB-measures, Physica D 103 (1997) 18-33.
7. R. Coutinho, Dynâmica simbólica linear, PhD Thesis, Departamento de Matemática, IST Lisbon (1999).
8. D. Daems, Probabilistic and thermodynamic aspects of dynamical systems, PhD Thesis, Université libre de Bruxelles (1998).
9. G. Gielis and R.S. MacKay, Coupled map lattices with phase transitions, Nonlinearity 13 (2000) 867-888.
10. E. Järvenpää and M. Järvenpää, On the definition of SRB-measures for coupled map lattices, Commun. Math. Phys. 220 (2001) 1-12.
11. M. Jiang and Y. Pesin, Equilibrium measures for coupled map lattices: existence, uniqueness and finite-dimensional approximations, Comm. Math. Phys. 193 (1998) 675-711.
12. K. Kaneko (ed.), Theory and applications of coupled map lattices, Wiley (1993).
13. A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge University Press (1995).
14. G. Keller, M. Künzle and T. Nowicki, Some phase transitions in coupled map lattices, Physica D 59 (1992) 39-51.
15. A. Pikovsky, M. Rosenblum and J. Kurths, Synchronization. A universal concept in nonlinear sciences, Cambridge University Press (2001).
16. D. Rand, The topological classification of Lorenz attractors, Math. Proc. Camb. Phil. Soc. 83 (1978) 451-460.
17. C. Robinson, Dynamical systems, 2nd edition, CRC Press (1999).
18. J. Schmeling, Entropy preservation under markov coding, J. Stat. Phys. 104 (2001) 799-815.