Cycle Expansions for Intermittent Maps

Progress of Theoretical Physics Supplement

Volumn 150, Issue , 2003, Pages 1-21

  Artuso, Roberto ^a   Cvitanović, Predrag ^b   Tanner, Gregor ^c  

^a UNIVERSITY OF INSUBRIA   (Italy)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c HEWLETT PACKARD LABORATORIES   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344118114     PISSN: 03759687     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTPS.150.1     Document Type: Conference Paper

References (44)

1. P. Manneville and Y. Pomeau, Phys. Lett. A 75 (1979), 1.
2. Y. Pomeau and P. Manneville, Commun. Math. Phys. 74 (1980), 189.
3. R. S. MacKay and J. D. Miess, Hamiltonian Dynamical Systems (Adam Hilger, Bristol, 1987).
4. D. H. Mayer, Bull. Soc. Math. France 104 (1976), 195.
5. D. Mayer and G. Roepstorff, J. Stat. Phys. 47 (1987), 149.
6. R. Artuso, P. Cvitanović and B. G. Kenny, Phys. Rev. A 39 (1989), 268.
7. P. Cvitanović, in Non-linear Evolution and Chaotic Phenomena, ed. P. Zweifel, G. Gallavotti and M. Anile (Plenum, New York 1987), p. 349.
8. P. Cvitanović, in Number Theory and Physics, Les Houches 1989 Spring School, ed. C. Itzykson, P. Moussa and M. Waldschmidt (Springer, New York, 1992).
9. R. Artuso, E. Aurell and P. Cvitanović, Nonlinearity 3 (1990), 361.
10. D. H. Mayer, Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, ed. T. Bedford, M. Keane and C. Series (Oxford University Press, Oxford, 1991).
11. P. Cvitanović, K. Hansen, J. Rolf and G. Vattay, Nonlinearity 11 (1998), 1209.
12. G. Tanner and D. Wintgen, Phys. Rev. Lett. 75 (1995), 2928.
13. G. Tanner, K. T. Hansen and J. Main, Nonlinearity 9 (1996), 1641.
14. G. Tanner, J. of Phys. A 30 (1997), 2863.
15. D. Ruelle, Statistical Mechanics, Thermodynamic Formalism (Addison-Wesley, Reading MA, 1978).
16. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge Univ. Press, Cambridge, 1997).
17. P. Cvitanović, R. Artuso, P. Dahlqvist, R. Mainieri, G. Tanner, G. Vattay, N. Whelan and A. Wirzba, Chaos: Classical and Quantum (www.nbi.dk/ChaoeBook/ 2003)
18. H. H. Rugh, Nonlinearity 5 (1992), 1237.
19. P. Cvitanović, P. E. Rosenqvist, H. H. Rugh and G. Vattay, Chaos 3 (1993), 619.
20. C. P. Dettmann and P. Cvitanović, Phys. Rev. E 56 (1997), 6687; "Stability ordering of cycle expansions" section of Ref. 17).
21. C. P. Dettmann and P. Cvitanović, Phys. Rev. E 56 (1997), 6687; "Stability ordering of cycle expansions" section of Ref. 17).
22. P. Dahlqvist, J. of Phys. A 27 (1994), 763.
23. P. Dahlqvist, Nonlinearity 8 (1995), 11.
24. P. Cvitanović, Phys. Rev. Lett. 61 (1988), 2729.
25. R. Artuso, E. Aurell and P. Cvitanović, Nonlinearity 3 (1990), 325.
26. H. H. Rugh, Inv. Math. 135 (1999), 1.
27. S. Isola, J. Stat. Phys. 97 (1999), 263.
28. S. Isola, Nonlinearity 15 (2002), 1521.
29. T. Prellberg, nlin.CD/0108044.
30. T. Prellberg, Maps of the interval with indifferent fixed points: thermodynamic formalism and phase transitions, Ph.D. Thesis (Virginia Polytechnic Inst., 1991).
31. T. Prellberg and J. Slawny, J. Stat. Phys. 66 (1992), 503.
32. P. Gaspard and X.-J. Wang, Proc. Natl. Acad. Sci. U.S.A. 85 (1988), 4591.
33. X.-J. Wang, Phys. Rev. A 40 (1989), 6647; Phys. Rev. A 39 (1989), 3214.
34. X.-J. Wang, Phys. Rev. A 40 (1989), 6647; Phys. Rev. A 39 (1989), 3214.
35. B. Fornberg and K. S. Kölbig, Math. of Computation 29 (1975), 582.
36. A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher trancendental functions, Vol. I (McGraw-Hill, New York, 1953).
37. The proof of the bound (3-14) can be found in P. Dahlqvist's unpublished notes, www.nbi.dk/ChaosBook/extras/PDahlqvistEscape.ps.gz.
38. Z. Kaufmann, H. Lustfeld and J. Bene, Phys. Rev. E 53 (1996), 1416.
39. P. Dahlqvist, J. of Phys. A 30 (1997), L351.
40. S. F. Nielsen, P. Dahlqvist and P. Cvitanović, J. of Phys. A 32 (1999), 6757.
41. P. Dahlqvist, Phys. Rev. E 60 (1999), 6639.
42. For an introduction to Tauberian theorems for power series and Laplace transforms see: W. Feller, An introduction to probability theory and applications, Vol. II (Wiley, New York, 1966).
43. R. Artuso, G. Casati and R. Lombardi, Phys. Rev. Lett. 71 (1993), 62.
44. Section Marginal stability and anomalous diffusion, Ref. 17).