Stability of the spectrum for transfer operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 1, pp. 141-152.
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     title = {Stability of the spectrum for transfer operators},
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     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_1_141_0/}
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Keller, Gerhard; Liverani, Carlangelo. Stability of the spectrum for transfer operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 1, pp. 141-152. http://www.numdam.org/item/ASNSP_1999_4_28_1_141_0/

[1] V. Baladi - M. Holschneider, Approximation of nonessential spectrum of transfer operators, Preprint (1998). | MR

[2] V. Baladi - L.S. Young, On the spectra of randomly perturbed expanding maps, Comm. Math. Phys. 156 (1993), 355-385; 166 (1994), 219-220. | MR | Zbl

[3] M.L. Blank, Stochastic properties of deterministic dynamical systems, Soviet Sci. Rev. Sect. C Math. Phys. Rev. 6 (1987), 243-271. | MR | Zbl

[4] M.L. Blank, Small perturbations of chaotic dynamical systems, Uspekhi Mat. Nauk 44 (1989), 3-28. | MR | Zbl

[5] M.L. Blank - G. Keller, Stochastic stability versus localization in chaotic dynamical systems, Nonlinearity 10 (1997), 81-107. | MR | Zbl

[6] M.L. Blank - G. Keller, Random perturbations of chaotic dynamical systems: Stability of the spectrum, Preprint (1998). | MR

[7] A. Boyarsky - P. Góra, Absolutely continuous invariant measures for piecewise expanding C2 transformations in RN, Israel J. Math. 67 (1989), 272-286. | MR | Zbl

[8] A. Boyarsky - P. Góra, "Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension ", Birkhäuser, Boston, 1997. | MR | Zbl

[9] C. Chiu - Q. Du - T.Y. Li, Error estimates of the Markov finite approximation to the Frobenius-Perron operator, Nonlinear Anal. 19 (1992), 291-308. | MR | Zbl

[10] N. Dunford - J.T. Schwartz, "Linear Operators, Part I: General Theory", Wiley, 1957. | MR | Zbl

[11] G. Froyland, Computer-assisted bounds for the rate of decay of correlations, Comm. Math. Phys. 189 (1997), 237-257. | MR | Zbl

[12] H. Hennion, Sur un théorème spectral et son application aux noyaux Lipchitziens, Proc. Amer. Math. Soc. 118 (1993), 627-634. | MR | Zbl

[13] F. Hofbauer - G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z. 180 (1982), 119-140. | MR | Zbl

[14] F.Y. Hunt - W. Miller, On the approximation of invariant measures, J. Statist. Phys. 66 (1992), 535-548. | MR | Zbl

[15] C.T. Ionescu Tulcea - G. Marinescu, Thórie ergodique pour des classes d'opérations non complètement continues, Ann. of Math. 52 (1950), 140-147. | MR | Zbl

[16] M. Iosifescu - R. Theodorescu, "Random Processes and Learning", Grundlehren Math. Wiss., Vol. 150, Springer, 1969. | MR | Zbl

[17] M. Keane - R. Murray - L.S. Young, Computing invariant measures for expanding circle maps, Nonlinearity 11 (1998), 27-46. | MR | Zbl

[18] G. Keller, Ergodicité et mesures invariantes pour les transformations dilatantes par morceaux d'une région bornée du plan, C.R.Acad. Sci. Paris, Série A 289 (1979), 625-627 (Kurzfassung der Dissertation). | MR | Zbl

[19] G. Keller, Un théorème de la limite centrale pour une classe de transformations monotones par morceaux, C. R. Acad. Sci. Paris, Série A, 291 (1980), 155-158. | MR | Zbl

[20] G. Keller, On the rate of convergence to equilibrium in one-dimensional systems, Comm. Math. Phys. 96 (1984), 181-193. | MR | Zbl

[21] G. Keller, Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982), 313-333. | MR | Zbl

[22] G. Keller - M. Künzle, Transfer operators for coupled map lattices, Ergodic Theory Dynam. Systems 12 (1992), 297-318. | MR | Zbl

[23] G. Keller - T. Nowicki, Spectral theory, zeta functions and the distribution of periodic orbits for Collet-Eckmann maps, Comm. Math. Phys. 149 (1992), 31-69. | MR | Zbl

[24] A. Lasota - J.A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481-488. | MR | Zbl

[25] T.Y. Li, Finite approximations for the Frobenius-Perron operator: A solution to Ulam's conjecture, J. Approx. Theory 17 (1976), 177-186. | MR | Zbl

[26] W. Miller, Stability and approximation of invariant measures for a class of nonexpanding transformations, Nonlinear Anal. 23 (1994), 1013-1025. | MR | Zbl

[27] M.F. Norman, "Markov Processes and Learning Models", Mathematics in Science and Engineering, Vol. 84, Academic Press, 1972. | MR | Zbl

[28] W. Parry - M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, Vol. 187-188, 1990. | Numdam | MR | Zbl

[29] A. Pinkus, "n-Widths in Approximation Theory", Springer, 1985. | MR | Zbl

[30] M. Rychlik, Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80. | MR | Zbl

[31] H.H. Schaefer, "Banach Lattices and Positive Operators", Grundlehren Math. Wiss., Vol. 215, Springer, 1974. | MR | Zbl