On the spectrum of Farey and Gauss maps

Nonlinearity

Volumn 15, Issue 5, 2002, Pages 1521-1539

  Isola, Stefano ^a  

^a UNIVERSITY OF CAMERINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041629642     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/5/310     Document Type: Article

References (34)

1. [Ba1] Baladi V 2000 Positive Transfer Operators and Decay of Correlations (Singapore: World Scientific)
2. [Ba2] Baladi V 1997 Dynamical zeta functions Real and Complex Dynamical Systems ed B Branner and P Hjorth (Dordrecht: Kluwer)
3. [Bi] Billingsley P 1964 Ergodic Theory and Information (New York: Wiley)
4. [C] Collet P 1996 Some ergodic properties of maps of the interval Dynamical Systems: Proc. first UNESCO CIMPA School of Dynamics and Disordered Systems (Temuco, Chile, 1991) (Bristol: Hermann)
5. [CI] Collet P and Isola S 1991 On the essential spectrum of the transfer operator for expanding Markov maps Commun. Math. Phys. 139 551-7
6. [DeV] DeVito C L 1990 Functional Analysis and Linear Operator Theory (Reading, MA: Addison-Wesley)
7. [D] Dodds P 1993 Master's Thesis The University of Melbourne
8. [DS] Dunford N and Schwartz J T 1963 Linear Operators (part I) (New York: Interscience)
9. [GR] Gradshteyn I and Ryzhik I 1965 Table of Integrals, Series and Products (New York: Academic)
10. [E] Erdèly A et al 1953-5 Higher Trascendental Functions (Bateman Manuscript Project vol I-III) (New York: McGraw-Hill)
11. [F] Feigenbaum M 1988 J. Stat. Phys. 52 527-69
12. [G] Grothendieck A 1956 La theorie de Fredholm Bull. Soc. Math. Fr. 84 319-84
13. [GK] Goheberg G C and Krejn MG 1971 Introduction à la théorie des opérateurs linéaires non auto-adjoints dans un espace (Paris: Hilbertien Dunod)
14. [HR] Hardy G H and Wright E M 1979 An Introduction to the Theory of Numbers (Oxford: Clarendon)
15. [HI] Haydn N T A and Isola S 2001 Parabolic rational maps J. London Math. Soc. 63 673-89
16. [HY] Hu H and Young L-S 1995 Nonexistence of SRB measures for some systems that are 'almost Anosov' Erg Th. Dyn. Syst. 15 67-75
17. [Is] Isola S 2001 On systems with finite ergodic degree Preprint
18. [Ki] Khinchin A 1964 Continued Fractions (Chicago, IL: University of Chicago Press)
19. [Le] Lewis JB 1997 Spaces of holomorphic functions equivalent to the even Maass cusp forms Invent Math. 127 271-306
20. [Ma1] Mayer D H 1990 On the thermodynamic formalism for the Gauss map Commun. Math. Phys. 130 311-33
21. [Ma2] Mayer D H 1991 Continued fractions and related transformations Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces ed T Bedford, M Keane and C Series (Oxford: Oxford University Press)
22. [Ma3] Mayer D H 1976 On a ζ function related to the continued fraction transformation Bull. Soc. math. France 104 195-203
23. [MaR1] Mayer D H and Roepstorff G 1987 On the relaxation time of Gauss' continued fraction map: I. The Hubert space approach J. Stat. Phys. 47 149-71
24. [MaR2] Mayer D H and Roepstorff G 1988 On the relaxation time of Gauss'continued fraction map: II.The Banach space approach J. Stat. Phys. 50 331-44
25. [Me] Meunier C 1984 Continuity of type I intermittency from a measure theoretical point of view J. Stat. Phys 36 321-65
26. [PM] Pomeau Y and Manneville P 1980 Intermittent transition to turbulence in dissipative dynamical systems Comm. Math. Phys. 74 189-97
27. [P1] Prellberg T 1991 PhD Thesis Virginia Tech
28. Prellberg T 2001 Preprint
29. [PS] Prellberg T and Slawny J 1992 Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions J. Stat. Phys. 66 503-14
30. [Rue] Ruelle D 1976 Zeta functions for expanding maps and Anosov flows Invent. Math. 34 231-42
31. [Rug] Rugh H H 1999 Intermittency and regularized Fredholm determinants Invent. Math, 135 1-24
32. [Sne] Sneddon IN 1974 The Use of Integral Transforms (New Delhi: Tata McGraw-Hill)
33. [Tit1] Titchmarsh E C 1939 The Theory of Functions (Oxford: Oxford University Press)
34. [Tit2] Titchmarsh E C 1937 Introduction to the Theory of Fourier Integrals (Oxford: Clarendon)