Zeta functions and transfer operators for multidimensional piecewise affine and expanding maps

Ergodic Theory and Dynamical Systems

Volumn 21, Issue 3, 2001, Pages 689-716

  Buzzi, Jérôme ^a   Keller, Gerhard ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035608682     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385701001341     Document Type: Article

References (24)

1. V. Baladi and G. Keller. Zeta-functions and transfer operators for piecewise monotone transformations. Commun. Math. Phys. 127 (1990), 459-478.
2. M. Berger. Geometry. Springer, Berlin, 1987
3. M. Blank. Stochastic properties of deterministic dynamical systems. Sov. Sci. Rev. C Maths/Phys. 6 (1987), 243-271.
4. M. Blank. Discreteness and Continuity in Problems of Chaotic Dynamics (Translations of Mathematical Monographs, 161). American Mathematical Society, 1997.
5. J. Buzzi. Entropies et représentation markovienne des applications régulières de l'intervalle. Thèse, Université Paris-Sud, Orsay, 1995.
6. d. Monat. Math. 124 (1997), 97-118.
7. J. Buzzi. Markov extensions for multi-dimensional dynamical systems. Israel J. Math. 112 (1999), 357-380.
8. J. Buzzi. A.c.i.m.'s for arbitrary expanding piecewise real-analytic mappings of the plane. Ergod. Th. & Dynam. Sys. 20 (2000), 697-708.
9. J. Buzzi. Thermodynamical Formalism for Multi-dimensional Piecewise Invertible Maps, Seattle, 1999 (Proc. Symp. Pure Applied Math.). American Mathematical Society.
10. J. Buzzi. Absolutely continuous invariant measures for generic multidimensional piecewise affine expanding maps. Int. J. Bif. Chaos 9 (1999), 1743-1750.
11. L. C. Evans and R. F. Gariepy. Measure Theory and Fine Properties of Functions. CRC Press, 1992.
12. E. Giusti. Minimal Surfaces and Functions of Bounded Variation. Boston, Birkhäuser, 1984.
13. F. Hofbauer. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 34 (1979), 213-237. F. Hofbauer. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 38 (1981), 107-115.
14. F. Hofbauer. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 34 (1979), 213-237. F. Hofbauer. On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. Israel J. Math. 38 (1981), 107-115.
15. F. Hofbauer and G. Keller. Zeta functions and transfer operators for piecewise linear transformations. J. reine angew. Math. 352 (1984), 100-113.
16. G. Keller. Ergodicité et mesures invariantes pour les transformations dilatantes par morceaux d'une région bornée du plan. C. R. Acad. Sci. Paris A 289 (1979), 625-627.
17. G. Keller. Generalized bounded variation and applications to piecewise monotonic transformations. Z. Wahrsch. Verw. Gebiete 69 (1985), 461-478.
18. G. Keller. Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems. Trans. Amer. Math. Soc. 314 (1989), 433-497.
19. k. Tokyo J. Math. 18 (1995), 401-416.
20. M. Mori. Fredholm determinant for piecewise linear transformations on a plane. Tokyo J. Math. 21 (1998), 477-510.
21. B. Saussol. Absolutely continuous invariant measures for multidimensional expanding maps. Israel J. Math. 116 (2000), 223-248.
22. M. Tsujii. Absolutely continuous invariant measures for piecewise real-analytic expanding maps on the plane. Commun. Math. Phys. 208 (2000), 605-622.
23. W. Ziemer. Weakly Differentiable Functions (Graduate Texts in Mathematics, 120). Springer, Berlin, 1989.
24. M. Tsujii. Absolutely continuous invariant measures for expanding piecewise linear maps. Invent. Math. to appear.