@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}, pages = {141--152}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 28}, number = {1}, year = {1999}, zbl = {0956.37003}, mrnumber = {1679080}, language = {en}, url = {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, Tome 28 (1999) no. 1, pp. 141-152. http://www.numdam.org/item/ASNSP_1999_4_28_1_141_0/
[1] Approximation of nonessential spectrum of transfer operators, Preprint (1998). | MR 1690191
- ,[2] 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] Stochastic properties of deterministic dynamical systems, Soviet Sci. Rev. Sect. C Math. Phys. Rev. 6 (1987), 243-271. | MR 968674 | Zbl 0634.58019
,[4] Small perturbations of chaotic dynamical systems, Uspekhi Mat. Nauk 44 (1989), 3-28. | MR 1037009 | Zbl 0702.58063
,[5] Stochastic stability versus localization in chaotic dynamical systems, Nonlinearity 10 (1997), 81-107. | MR 1430741 | Zbl 0907.58011
- ,[6] Random perturbations of chaotic dynamical systems: Stability of the spectrum, Preprint (1998). | MR 1644405
- ,[7] Absolutely continuous invariant measures for piecewise expanding C2 transformations in RN, Israel J. Math. 67 (1989), 272-286. | MR 1029902 | Zbl 0691.28004
- ,[8] Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension ", Birkhäuser, Boston, 1997. | MR 1461536 | Zbl 0893.28013
- , "[9] Error estimates of the Markov finite approximation to the Frobenius-Perron operator, Nonlinear Anal. 19 (1992), 291-308. | MR 1178404 | Zbl 0788.28009
- - ,[10] Linear Operators, Part I: General Theory", Wiley, 1957. | MR 1009162 | Zbl 0635.47001
- , "[11] Computer-assisted bounds for the rate of decay of correlations, Comm. Math. Phys. 189 (1997), 237-257. | MR 1478538 | Zbl 0892.58047
,[12] Sur un théorème spectral et son application aux noyaux Lipchitziens, Proc. Amer. Math. Soc. 118 (1993), 627-634. | MR 1129880 | Zbl 0772.60049
,[13] Ergodic properties of invariant measures for piecewise monotonic transformations, Math. Z. 180 (1982), 119-140. | MR 656227 | Zbl 0485.28016
- ,[14] On the approximation of invariant measures, J. Statist. Phys. 66 (1992), 535-548. | MR 1149495 | Zbl 0892.58048
- ,[15] Thórie ergodique pour des classes d'opérations non complètement continues, Ann. of Math. 52 (1950), 140-147. | MR 37469 | Zbl 0040.06502
- ,[16] Random Processes and Learning", Grundlehren Math. Wiss., Vol. 150, Springer, 1969. | MR 293704 | Zbl 0194.51101
- , "[17] Computing invariant measures for expanding circle maps, Nonlinearity 11 (1998), 27-46. | MR 1492949 | Zbl 0903.58019
- - ,[18] 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] 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] On the rate of convergence to equilibrium in one-dimensional systems, Comm. Math. Phys. 96 (1984), 181-193. | MR 768254 | Zbl 0576.58016
,[21] Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982), 313-333. | MR 685377 | Zbl 0496.58010
,[22] Transfer operators for coupled map lattices, Ergodic Theory Dynam. Systems 12 (1992), 297-318. | MR 1176625 | Zbl 0737.58032
- ,[23] 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] On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481-488. | MR 335758 | Zbl 0298.28015
- ,[25] 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] Stability and approximation of invariant measures for a class of nonexpanding transformations, Nonlinear Anal. 23 (1994), 1013-1025. | MR 1304241 | Zbl 0822.28009
,[27] Markov Processes and Learning Models", Mathematics in Science and Engineering, Vol. 84, Academic Press, 1972. | MR 423546 | Zbl 0262.92003
, "[28] Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, Vol. 187-188, 1990. | MR 1085356 | Zbl 0726.58003
- ,[29] n-Widths in Approximation Theory", Springer, 1985. | MR 774404 | Zbl 0551.41001
, "[30] Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80. | MR 728198 | Zbl 0575.28011
,[31] Banach Lattices and Positive Operators", Grundlehren Math. Wiss., Vol. 215, Springer, 1974. | MR 423039 | Zbl 0296.47023
, "