Stability of the spectrum for transfer operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 28 (1999) no. 1, p. 141-152
@article{ASNSP_1999_4_28_1_141_0,
     author = {Keller, Gerhard and Liverani, Carlangelo},
     title = {Stability of the spectrum for transfer operators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {1},
     year = {1999},
     pages = {141-152},
     zbl = {0956.37003},
     mrnumber = {1679080},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_1_141_0}
}
Keller, Gerhard; Liverani, Carlangelo. Stability of the spectrum for transfer operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 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 1690191

[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 1233850 | Zbl 0809.60101

[3] M.L. Blank, Stochastic properties of deterministic dynamical systems, Soviet Sci. Rev. Sect. C Math. Phys. Rev. 6 (1987), 243-271. | MR 968674 | Zbl 0634.58019

[4] M.L. Blank, Small perturbations of chaotic dynamical systems, Uspekhi Mat. Nauk 44 (1989), 3-28. | MR 1037009 | Zbl 0702.58063

[5] M.L. Blank - G. Keller, Stochastic stability versus localization in chaotic dynamical systems, Nonlinearity 10 (1997), 81-107. | MR 1430741 | Zbl 0907.58011

[6] M.L. Blank - G. Keller, Random perturbations of chaotic dynamical systems: Stability of the spectrum, Preprint (1998). | MR 1644405

[7] A. Boyarsky - P. Góra, Absolutely continuous invariant measures for piecewise expanding C2 transformations in RN, Israel J. Math. 67 (1989), 272-286. | MR 1029902 | Zbl 0691.28004

[8] A. Boyarsky - P. Góra, "Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension ", Birkhäuser, Boston, 1997. | MR 1461536 | Zbl 0893.28013

[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 1178404 | Zbl 0788.28009

[10] N. Dunford - J.T. Schwartz, "Linear Operators, Part I: General Theory", Wiley, 1957. | MR 1009162 | Zbl 0635.47001

[11] G. Froyland, Computer-assisted bounds for the rate of decay of correlations, Comm. Math. Phys. 189 (1997), 237-257. | MR 1478538 | Zbl 0892.58047

[12] H. Hennion, Sur un théorème spectral et son application aux noyaux Lipchitziens, Proc. Amer. Math. Soc. 118 (1993), 627-634. | MR 1129880 | Zbl 0772.60049

[13] F. Hofbauer - G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z. 180 (1982), 119-140. | MR 656227 | Zbl 0485.28016

[14] F.Y. Hunt - W. Miller, On the approximation of invariant measures, J. Statist. Phys. 66 (1992), 535-548. | MR 1149495 | Zbl 0892.58048

[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 37469 | Zbl 0040.06502

[16] M. Iosifescu - R. Theodorescu, "Random Processes and Learning", Grundlehren Math. Wiss., Vol. 150, Springer, 1969. | MR 293704 | Zbl 0194.51101

[17] M. Keane - R. Murray - L.S. Young, Computing invariant measures for expanding circle maps, Nonlinearity 11 (1998), 27-46. | MR 1492949 | Zbl 0903.58019

[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 556443 | Zbl 0419.28007

[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 605005 | Zbl 0446.60013

[20] G. Keller, On the rate of convergence to equilibrium in one-dimensional systems, Comm. Math. Phys. 96 (1984), 181-193. | MR 768254 | Zbl 0576.58016

[21] G. Keller, Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982), 313-333. | MR 685377 | Zbl 0496.58010

[22] G. Keller - M. Künzle, Transfer operators for coupled map lattices, Ergodic Theory Dynam. Systems 12 (1992), 297-318. | MR 1176625 | Zbl 0737.58032

[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 1182410 | Zbl 0763.58024

[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 335758 | Zbl 0298.28015

[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 412689 | Zbl 0357.41011

[26] W. Miller, Stability and approximation of invariant measures for a class of nonexpanding transformations, Nonlinear Anal. 23 (1994), 1013-1025. | MR 1304241 | Zbl 0822.28009

[27] M.F. Norman, "Markov Processes and Learning Models", Mathematics in Science and Engineering, Vol. 84, Academic Press, 1972. | MR 423546 | Zbl 0262.92003

[28] W. Parry - M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, Vol. 187-188, 1990. | MR 1085356 | Zbl 0726.58003

[29] A. Pinkus, "n-Widths in Approximation Theory", Springer, 1985. | MR 774404 | Zbl 0551.41001

[30] M. Rychlik, Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80. | MR 728198 | Zbl 0575.28011

[31] H.H. Schaefer, "Banach Lattices and Positive Operators", Grundlehren Math. Wiss., Vol. 215, Springer, 1974. | MR 423039 | Zbl 0296.47023