The pulled Frenkel-Kontorova chain

Nonlinearity

Volumn 11, Issue 4, 1998, Pages 923-948

  Slijepcevic S ^a,b  

^a DAMTP   (United Kingdom)

^b UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042221340     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/11/4/010     Document Type: Article

References (28)

1. Aubry S and LeDaeron P 1983 The discrete Frenkel-Kontorova model and its extensions I. Exact results for the ground states Physica D 8 381-422
2. Aubry S, MacKay R S and Baesens C 1992 Equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for Frenkel-Kontorova models Physica D 56 123-34
3. Arnold V I (ed) 1994 Dynamical Systems vol V (New York: Springer)
4. Bangert V 1988 Mather sets for twist maps and geodesics on tori Dyn. Reported vol 1, ed U Kirchgraber and H O Walter (New York: Wiley)
5. Bangert V 1994 Geodesic rays, Busemann functions and monotone twist maps Calc. Variations Part. Dif. Eqns 2 49-63
6. Baesens C and MacKay R S 1998 Gradient dynamics of tilted Frenkel-Kontorova model Nonlinearity 11 949-64
7. Gradient Dynamics of tilted Frenkel-Kontorova model Nonlinearity submitted
8. Bak P, Tang C and Wiesenfeld K 1988 Self-organised criticality Phys. Rev. A 38 364-474
9. Dalecki J L and Krein M G 1974 Stability of Solutions of Differential Equations in Banach Space (Providence, RI: American Mathematical Society)
10. Doeff H E 1997 Rotation measures for homeomorphisms of the torus homotopic to a Dehn twist Ergod. Theor. Dynam. Syst. 17 575-91
11. Durrett R 1991 Probability: Theory and Examples (Belmont: Wodsworth and Brooks-Cole)
12. Khanin W E K, Mazel A and Sinai Y G 1998 Invariant measures for Burgers equation with random forcing, to be published. See also
13. Khanin W E K, Mazel A and Sinai Y G 1997 Phys. Rev. Lett. 78 1904-7
14. Elmer F J 1994 Avalanches in the weakly driven Frenkel-Kontorova model Phys. Rev. E 50 4470-87
15. Floria L M and Mazo J J 1996 Dissipative dynamics of the Frenkel-Kontorova model Adv. Phys. 45 505-98
16. Hirsch M 1982 Systems of differential equations which are competitive or cooperative I: Limit sets. SIAM J. Math. Anal. 13 167-79
17. Hubbard J H and West B H 1995 Differential Equations: A Dynamical System Approach (New York: Springer)
18. Jensen H J, Brechet Y and Doucot B 1993 Instabilities of an elastic chain in a random potential J. Physique I 3 611-23
19. Katok A and Hasselblatt B 1995 Introduction to the Modern Theory of Dynamical Systems (Cambridge: Cambridge University Press)
20. Lang S 1993 Real and Functional Analysis (New York: Springer)
21. Mather J 1991 Variational construction of orbits of twist dipheomorphisms J. Am. Math. Soc. 4 207-63
22. Middleton A and Fisher D S 1993 Critical-behavior of charge-density waves below threshold - numerical and scaling analysis Phys. Rev. B 47 3530-52
23. MacKay R S 1993 Renormalisation in Area-preserving Maps (Singapore: World Scientific)
24. MacKay R S and Stark J 1985 Lectures on orbits of minimal action for area-preserving maps Preprint University of Warwick
25. MacKay R S and Stark J 1992 Locally most robust circles and boundary circles for area-preserving maps Nonlinearity 5 867-88
26. Slijepčević S Gradient dynamics and connecting orbits of twist diffeomorphisms, in preparation
27. Smith H L 1995 Monotone Dynamical Systems, An Introduction to the Theory of Competetive and Cooperative Systems (Providence, RI: American Mathematical Society)
28. Takens F 1976 Constrained equations: a study of implicit differential equations and their discontinuous solutions Structural Stability, Theory of Catastrophe, and Applications (Lecture Notes in Mathematics 525) (New York: Springer) pp 143-234