Infinite kneading matrices and weighted zeta functions of interval maps

Journal of Functional Analysis

Volumn 128, Issue 1, 1995, Pages 226-244

  Baladi, Viviane ^a,b  

^a UNIVERSITÉ DE LYON   (France)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000807640     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1006/jfan.1995.1029     Document Type: Article

References (14)

1. V. Baladi and G. Keller, Zeta functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys. 127 (1990), 459-477.
2. V. Baladi and D. Ruelle, An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps, IHES preprint, Ergodic Theory Dynamical Systems 14 (1994), 621-632.
3. V. Baladi and D. Ruelle, Some properties of zeta functions associated with maps in one dimension, Appendix to V. Baladi, Dynamical zeta functions and generalised Fredholm determinants, in “Proceedings Xlth International Congress of Mathematical Physics, Paris (1994), ” to appear.
4. A. Grothendieck, La théorie de Fredholm, Bull. Soc. Math. France 84 (1956), 319-384.
5. F. Hofbauer and G. Keller, Zeta-functions and transfer-operators for piecewise linear transformations, J. Reine Angew. Math. 352 (1984), 100-113.
6. T. Kato, "Perturbation Theory for Linear Operators, ” 2nd ed., 2nd printing, Springer- Verlag, Berlin/Heidelberg/New York, 1984.
7. J. Milnor and W. Thurston, Iterated maps of the interval, in “Dynamical Systems (Maryland, 1986-1987)” (J. C. Alexander, Ed.), Lecture Notes in Mathematics, Vol. 1342, Springer-Verlag, Berlin/Heidelberg/New York, 1988.
8. M. Mori, Fredholm determinant for piecewise linear transformations, Osaka J. Math. 27 (1990), 81-116.
9. M. Mori, Fredholm determinant for piecewise monotonic transformations, Osaka J. Math. 29 (1992), 497-529.
10. M. Pollicott, Meromorphic extensions of generalised zeta functions, Invent. Math. 85 (1986), 147-164.
11. F. Riesz and B. Sz-Nagy, “Lefons d’analyse fonctionnelle, ” 3ème éd. Academie des Sciences de Hongrie, 1955.
12. D. Ruelle, Dynamical zeta functions for maps of the interval, Bull. Amer. Math. Soc. (N.S.) 30 (1994), 212-214.
13. D. Ruelle, “Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval, ” CRM Monograph Series, Vol. 4, Amer. Math. Soc., Providence, 1994.
14. D. Ruelle, Functional equation for dynamical zeta functions of Milnor-Thurston type, IHES preprint, 1993.