Rigorous numerical approximation of Ruelle-Perron-Frobenius operators and topological pressure of expanding maps

Nonlinearity

Volumn 21, Issue 9, 2008, Pages 1953-1966

  Terhesiu, Dalia ^a   Froyland, Gary ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 51849091830     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/9/001     Document Type: Article

References (27)

1. Baladi V 2000 Positive Transfer Operators and Decay of Correlations (Singapore: World Scientific)
2. Blank M, Keller G and Liverani C 2002 Ruelle-Perron-Frobenius spectrum for Anosov maps Nonlinearity 15 1905-73
3. Buzzi J, Paccaut F and Schmitt B 2001 Conformal measures for multidimensional piecewise invertible maps Ergod. Theory Dyn. Syst. 21 1035-49
4. Denker M and Urbanski M 1991 On the existence of conformal measures Trans. Am. Math. Soc. 328 563-87
5. Ding J and Zhou A 1996 Finite approximations of Frobenius-Perron operators: a solution of Ulam's conjecture to multi-dimensional transformations Physica D 92 61-8
6. Feigenbaum J M, Proccaccia I and Tel T 1989 Scaling properties of multifractals as an eigenvalue problem Phys. Rev. A 39 5359-72
7. Froyland G 1995 Finite approximation of Sinai-Bowen-Ruelle measures for Anosov systems in two dimensions Random Comput. Dyn. 3 251-64
8. Froyland G, Murray R and Terhesiu D 2007 Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension Phys. Rev. E 76 036702
9. Giusti E 1984 Minimal Surfaces and Functions of Bounded Variation (Monographs in Mathematics vol 80) (Boston, MA: Birkhäuser)
10. Hofbauer F and Keller G 1982 Equilibrium states for piecewise monotonic transformations Ergod. Theory Dyn. Syst. 2 23-43
11. Kaufmann Z, Lustfeld H and Bene J 1996 Eigenvalue spectrum of the Frobenius-Perron operator near intermittency Phys. Rev. E 53 1416-21
12. Li T-Y 1976 Finite approximation for the Frobenius-Perron operator: a solution to Ulam's conjecture J. Approx. Theory 17 177-86
13. Liverani C 1995 Decay of correlations Ann. Math. 142 239-301
14. Liverani C, Saussol B and Vaienti S 1998 Conformal measures and decay of correlations for covering weighted systems Ergod. Theory Dyn. Syst. 18 1399-420
15. Murray R 1997 Discrete approximation of invariant densities PhD Thesis University of Cambridge
16. Murray R 1998 Approximation error for invariant density calculations Discrete Continuous Dyn. Syst. 4 535-58
17. Prellberg T 2003 Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions J. Stat. Phys. 66 503-14
18. Prellberg T 2003 Towards a complete determination of the spectrum of a transfer operator associated with intermittency J. Phys. A: Math. Gen. 36 2455-2461
19. Ruelle D 1968 Statistical mechanics of a one-dimensional lattice gas Commun. Math. Phys. 9 267-78
20. Ruelle D 1992 Thermodynamic formalism for maps satisfying positive expansiveness and specification Nonlinearity 5 1223-6
21. Ruelle D 2004 Thermodynamical Formalism 2nd edn (Cambridge: Cambridge University Press)
22. Sarig O 1999 Thermodynamic formalism for countable Markov shifts Ergod. Theory Dyn. Syst. 19 1565-93
23. Sarig O 2001 Phase transitions for countable topological Markov shifts Commun. Math. Phys. 217 555-77
24. Ulam S 1960 A Collection of Mathematical Problems (New York: Interscience)
25. Wang X J 1989 Statistical physics of temporal intermittency Phys. Rev. A 40 6647-61
26. Yuri M 1997 On the convergence to equilibrium states for certain non-hyperbolic systems Ergod. Theory Dyn. Syst. 17 977-1000
27. Yuri M 2003 Thermodynamic formalism for countable to one Markov systems Trans. Am. Math. Soc. 355 2949-71