Good Banach Spaces for Piecewise Hyperbolic Maps Via Interpolation

Baladi, Viviane; GouëZel, SéBastien

Baladi, Viviane ; GouëZel, SéBastien

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 1453-1481 / Harvested from Numdam

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Publié le : 2009-01-01

MR 2542733 | Zbl pre05590492 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2009.01.001

@article{AIHPC_2009__26_4_1453_0,
     author = {Baladi, Viviane and Gou\"eZel, S\'eBastien},
     title = {Good Banach Spaces for Piecewise Hyperbolic Maps Via Interpolation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {1453-1481},
     doi = {10.1016/j.anihpc.2009.01.001},
     mrnumber = {2542733},
     zbl = {pre05590492},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_4_1453_0}
}

Baladi, Viviane; GouëZel, SéBastien. Good Banach Spaces for Piecewise Hyperbolic Maps Via Interpolation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 1453-1481. doi : 10.1016/j.anihpc.2009.01.001. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_4_1453_0/

Bibliographie

[1] Alinhac S., Gérard P., Opérateurs Pseudo-Différentiels Et Théorème De Nash-Moser, CNRS éditions, Paris, 1991. | Zbl 0791.47044

[2] Baghdasaryan A. G., On the Intermediate Spaces and Quasi-Linearizability of a Pair of Spaces of Sobolev-Liouville Type, Anal. Math. 24 (1998) 3-14, (in Russian). | MR 1612065 | Zbl 0911.46020

[3] Baillif M., Baladi V., Kneading Determinants and Spectra of Transfer Operators in Higher Dimensions: the Isotropic Case, Ergodic Theory Dynam. Systems 25 (2005) 1437-1470. | MR 2173427 | Zbl 1085.37015

[4] Baladi V., Anisotropic Sobolev Spaces and Dynamical Transfer Operators: $C^{\infty}$ Foliations, in: Kolyada S., Manin Y., Ward T. (Eds.), Algebraic and Topological Dynamics, Contemp. Math., Amer. Math. Soc., 2005, pp. 123-136. | MR 2180233 | Zbl 1158.37304

[5] Baladi V., Tsujii M., Anisotropic Hölder and Sobolev Spaces for Hyperbolic Diffeomorphisms, Ann. Inst. Fourier 57 (2007) 127-154. | Numdam | MR 2313087 | Zbl 1138.37011

[6] Baladi V., Tsujii M., Dynamical Determinants and Spectrum for Hyperbolic Diffeomorphisms, in: Burns K., Dolgopyat D., Pesin Ya. (Eds.), Probabilistic and Geometric Structures in Dynamics, Contemp. Math., vol. 469, Amer. Math. Soc., 2008, pp. 29-68, Volume in honour of M. Brin's 60th birthday. | MR 2478465 | Zbl 1154.37320

[7] Billinsgley P., Convergence of Probability Measures, John Wiley and Sons, New York, 1968. | MR 233396 | Zbl 0172.21201

[8] Blank M., Keller G., Liverani C., Ruelle-Perron-Frobenius Spectrum for Anosov Maps, Nonlinearity 15 (2002) 1905-1973. | MR 1938476 | Zbl 1021.37015

[9] Buzzi J., Intrinsic Ergodicity of Affine Maps in ${[0, 1]}^{d}$ , Monatsh. Math. 124 (1997) 97-118. | MR 1462857 | Zbl 0886.58024

[10] Buzzi J., Absolutely Continuous Invariant Probability Measures for Arbitrary Expanding Piecewise R-Analytic Mappings of the Plane, Ergodic Theory Dynam. Systems 20 (2000) 697-708. | MR 1764923 | Zbl 0973.37003

[11] Buzzi J., No Or Infinitely Many a.C.I.P. for Piecewise Expanding $C^{r}$ Maps in Higher Dimensions, Comm. Math. Phys. 222 (2001) 495-501. | MR 1888086 | Zbl 1001.37003

[12] Buzzi J., Maume-Deschamps V., Decay of Correlations for Piecewise Invertible Maps in Higher Dimensions, Israel J. Math. 131 (2002) 203-220. | MR 1942309 | Zbl 1014.37017

[13] Chernov N. I., Ergodic and Statistical Properties of Piecewise Linear Hyperbolic Automorphisms of the 2-Torus, J. Statist. Phys. 69 (1992) 111-134. | MR 1184772 | Zbl 0925.58072

[14] Chernov N., Decay of Correlations and Dispersing Billiards, J. Statist. Phys. 94 (1999) 513-556. | MR 1675363 | Zbl 1047.37503

[15] Collet P., Eckmann J.-P., Liapunov Multipliers and Decay of Correlations in Dynamical Systems, J. Statist. Phys. 115 (2004) 217-254. | MR 2070095 | Zbl 1157.37306

[16] Cowieson W. J., Stochastic Stability for Piecewise Expanding Maps in $R^{d}$ , Nonlinearity 13 (2000) 1745-1760. | MR 1781816 | Zbl 0963.37004

[17] Cowieson W. J., Absolutely Continuous Invariant Measures for Most Piecewise Smooth Expanding Maps, Ergodic Theory Dynam. Systems 22 (2002) 1061-1078. | MR 1926276 | Zbl 1014.37016

[18] Demers M., Liverani C., Stability of Statistical Properties in Two-Dimensional Piecewise Hyperbolic Maps, Trans. Amer. Math. Soc. 360 (2008) 4777-4814. | MR 2403704 | Zbl 1153.37019

[19] Góra P., Boyarsky A., Absolutely Continuous Invariant Measures for Piecewise Expanding $C^{2}$ Transformation in $R^{N}$ , Israel J. Math. 67 (1989) 272-286. | MR 1029902 | Zbl 0691.28004

[20] Gouëzel S., Liverani C., Banach Spaces Adapted to Anosov Systems, Ergodic Theory Dynam. Systems 26 (2006) 189-218. | MR 2201945 | Zbl 1088.37010

[21] Gouëzel S., Liverani C., Compact Locally Maximal Hyperbolic Sets for Smooth Maps: Fine Statistical Properties, J. Differential Geometry 79 (2008) 433-477. | MR 2433929 | Zbl 1166.37010

[22] Hennion H., Sur Un Théorème Spectral Et Son Application Aux Noyaux Lipschitziens, Proc. Amer. Math. Soc. 118 (1993) 627-634. | MR 1129880 | Zbl 0772.60049

[23] Keller G., Ergodicité Et Mesures Invariantes Pour Les Transformations Dilatantes Par Morceaux D'une Région Bornée Du Plan, C. R. Acad. Sci. Paris Sér. A-B 289 (1979) A625-A627. | MR 556443 | Zbl 0419.28007

[24] Runst T., Sickel W., Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, Walter de Gruyter & Co., Berlin, 1996. | MR 1419319 | Zbl 0873.35001

[25] Saussol B., ACIMs for Multidimensional Expanding Maps, Israel J. Math. 116 (2000) 223-248. | MR 1759406 | Zbl 0982.37003

[26] Strichartz R., Multipliers on Fractional Sobolev Spaces, J. Math. Mech. 16 (1967) 1031-1060. | MR 215084 | Zbl 0145.38301

[27] Triebel H., General Function Spaces III (Spaces $B_{p, q}^{g (x)}$ and $F_{p, q}^{g (x)}$ , $1 < p < \infty$ : Basic Properties), Anal. Math. 3 (1977) 221-249. | MR 628468 | Zbl 0374.46027

[28] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. | MR 503903 | Zbl 0387.46032

[29] Triebel H., Theory of Function Spaces II, Birkhäuser, Basel, 1992. | MR 1163193 | Zbl 0763.46025

[30] Tsujii M., Piecewise Expanding Maps on the Plane With Singular Ergodic Properties, Ergodic Theory Dynam. Systems 20 (2000) 1851-1857. | MR 1804960 | Zbl 0992.37018

[31] Tsujii M., Absolutely Continuous Invariant Measures for Piecewise Real-Analytic Expanding Maps on the Plane, Comm. Math. Phys. 208 (2000) 605-622. | MR 1736328 | Zbl 0989.37015

[32] Tsujii M., Decay of Correlations in Suspension Semi-Flows of Angle-Multiplying Maps, Ergodic Theory Dynam. Systems 28 (2008) 291-317. | MR 2380311 | Zbl 1171.37318

[33] Volevich L. R., Paneyakh B. P., Certain Spaces of Generalised Functions and Embedding Theorems, Uspekhi Mat. Nauk 20 (1965) 3-74, English translation:, Russian Math. Surveys 20 (1965). | MR 174970 | Zbl 0135.16501

[34] Young L.-S., Statistical Properties of Dynamical Systems With Some Hyperbolicity, Ann. of Math. 147 (1998) 585-650. | MR 1637655 | Zbl 0945.37009