no. 3
Transfer operator for piecewise affine approximations of interval maps
Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 3, pp. 251-265 
@article{AIHPA_1995__62_3_251_0,
     author = {Baladi, Viviane and Isola, Stefano and Schmitt, Bernard},
     title = {Transfer operator for piecewise affine approximations of interval maps},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {251--265},
     year = {1995},
     publisher = {Gauthier-Villars},
     volume = {62},
     number = {3},
     mrnumber = {1335058},
     zbl = {0827.58014},
     language = {en},
     url = {https://www.numdam.org/item/AIHPA_1995__62_3_251_0/}
}
TY  - JOUR
AU  - Baladi, Viviane
AU  - Isola, Stefano
AU  - Schmitt, Bernard
TI  - Transfer operator for piecewise affine approximations of interval maps
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1995
SP  - 251
EP  - 265
VL  - 62
IS  - 3
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPA_1995__62_3_251_0/
LA  - en
ID  - AIHPA_1995__62_3_251_0
ER  - 
%0 Journal Article
%A Baladi, Viviane
%A Isola, Stefano
%A Schmitt, Bernard
%T Transfer operator for piecewise affine approximations of interval maps
%J Annales de l'I.H.P. Physique théorique
%D 1995
%P 251-265
%V 62
%N 3
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPA_1995__62_3_251_0/
%G en
%F AIHPA_1995__62_3_251_0
Baladi, Viviane; Isola, Stefano; Schmitt, Bernard. Transfer operator for piecewise affine approximations of interval maps. Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 3, pp. 251-265. https://www.numdam.org/item/AIHPA_1995__62_3_251_0/

[1] V. Baladi, Infinite kneading matrices and weighted zeta functions of interval maps, Preprint, 1933, to appear in J. Funct. Anal. | MR

[2] V. Baladi and G. Keller, Zeta functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys., Vol. 127, 1990, pp. 459-477. | Zbl | MR

[3] V. Baladi and L.-S. Young, On the spectra of randomly perturbed expanding maps, Comm. Math. Phys., Vol. 156, 1993, pp. 355-385. (See also Erratum, Comm. Math. Phys., Vol. 166, 1994, pp. 219-220.) | Zbl | MR

[4] P. Collet, Some ergodic properties of maps of the interval, Dynamical Systems and Frustrated Systems, R. Bamon, J.-M. Gambaudo and S. Martinez Eds., 1991 (to appear). | Zbl | MR

[5] I. Erdelyi and R. Lange, Spectral Decompositions on Banach Spaces, Lecture Notes in Math., Vol. 623, 1977. | Zbl | MR

[6] P. Gora and A. Boyarsky, Compactness of invariant densities for families of expanding, piecewise monotonic transformations, Can. J. Math., XLI, 1989, pp. 855-869. | Zbl | MR

[7] F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z., Vol. 180, 1982, pp. 119-140. | Zbl | MR

[8] T. Kato, Perturbation Theory for Linear Operators, Second printing of second ed., Springer-Verlag, Berlin, 1984.

[9] G. Keller, Stochastic stability in some chaotic dynamical systems, Mh. Math., Vol. 94, 1982, pp. 313-333. | Zbl | MR

[10] G. Keller, On the rate of convergence to equilibrium in one-dimensional dynamics, Comm. Math. Phys., Vol. 96, 1984, pp. 181-193. | Zbl | MR

[11] T.-Y. Li, Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture, J. of Approx. Theory, Vol. 17, 1976, pp. 177-186. | Zbl | MR

[12] W. De Melo and S. Van Strien, One-Dimensional Dynamics, Springer-Verlag, Berlin, 1993. | Zbl | MR

[13] D. Ruelle, Thermodynamic Formalism, Addison-Wesley, Reading, 1978. | Zbl | MR

[14] M. Rychlik, Bounded variation and invariant measures, Studia Math., Vol. LXXVI, 1983, pp. 69-80. | Zbl | MR

[15] M. Rychlik and E. Sorets, Regularity and other properties of absolutely continuous invariant measures for the quadratic family, Comm. Math. Phys., Vol. 150, 1992, pp. 217-236. | Zbl | MR

[16] H.J. Scholtz, Markov chains and discrete chaos, Physica, Vol. 4D, 1982, pp. 281-286., | MR

[17] S. Ulam, Problems in modern mathematics, Interscience Publishers, New York, 1960. | MR

[18] S. Wong, Some metric properties of piecewise monotonic mappings of the unit interval, Trans. Amer. Math. Soc., Vol. 246, 1978, pp. 493-500. | Zbl | MR