Citation: |
[1] |
V. Araujo, S. Galatolo and M.-J. Pacifico, Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors, Preprint arXiv:1204.0703. |
[2] |
V. Baladi, "Positive Transfer Operators & Decay of Correlation," 16 of Advanced Series in Nonlinear Dynamics. World Scientific, Singapore, 2000.doi: 10.1142/9789812813633. |
[3] |
V. Baladi, Anisotropic Sobolev spaces and dynamical transfer operators: $C^\infty$ foliations, Algebraic and Topological Dynamics, 123-135, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, (2005).doi: 10.1090/conm/385/07194. |
[4] |
V. Baladi and S. Gouëzel, Good Banach spaces for piecewise hyperbolic maps via interpolation, Ann. Inst. Henri Poincaré, Anal. Non. Lin., 26 (2009), 1453-1481.doi: 10.1016/j.anihpc.2009.01.001. |
[5] |
V. Baladi and S. Gouëzel, Banach spaces for piecewise cone hyperbolic maps, J. Modern Dynamics, 4 (2010), 91-137.doi: 10.3934/jmd.2010.4.91. |
[6] |
V. Baladi and C. Liverani, Exponential decay of correlations for piecewise cone hyperbolic contact flows, Communications in Mathematical Physics, 314 (2012), 689-773.doi: 10.1007/s00220-012-1538-4. |
[7] |
V. Baladi and M. Tsujii, Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms, Annales de L'Institut Fourier, 57 (2007), 127-154. |
[8] |
V. Baladi and M. Tsujii, Dynamical determinants and spectrum for hyperbolic diffeomorphisms, in "Probabilistic and Geometric Structures in Dynamics" (eds. K. Burns, D. Dolgopyat and Ya. Pesin ), Contemp. Math., Amer. Math. Soc., 469 (2008), 29-68.doi: 10.1090/conm/469/09160. |
[9] |
M. Blank, G. Keller and C. Liverani, Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity, 15 (2002), 1905-1973.doi: 10.1088/0951-7715/15/6/309. |
[10] |
O. Butterley, An alternative approach to generalised BV and the application to expanding interval maps, Discrete Contin. Dyn. Syst., 33 (2013), 3355-3363. |
[11] | |
[12] |
W. Cowieson, Absolutely continuous invariant measures for most piecewise smooth expanding maps, Ergodic Theory Dynam. Systems, 22 (2002), 1061-1078.doi: 10.1017/S0143385702000627. |
[13] |
M. Demers and C. Liverani, Stability of statistical properties in two-dimensional piecewise hyperbolic maps, Trans. Amer. Math. Soc., 360 (2008), 4777-4814.doi: 10.1090/S0002-9947-08-04464-4. |
[14] |
V. M. Gundlach and Y. Latushkin, A sharp formula for the essential spectral radius of the Ruelle transfer operator on smooth and Hölder spaces, Ergodic Theory Dynam. Systems, 23 (2003), 175-191.doi: 10.1017/S0143385702000962. |
[15] |
S. Gouëzel and C. Liverani, Banach spaces adapted to Anosov systems, Ergodic Theory Dynam. Systems, 26 (2006), 189-218.doi: 10.1017/S0143385705000374. |
[16] |
S. Gouëzel and C. Liverani, Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties, J. Diff. Geom., 79 (2008), 433-477. |
[17] |
M. Gromov, "Metric Structures for Riemannian and Non-Riemannian Spaces," 152 of Progress in Mathematics, Birkhäuser Boston Inc., Boston, MA, 1999. With Appendices by M. Katz, P. Pansu and S. Semmes. |
[18] |
G. Keller, Generalized bounded variation and applications to piecewise monotonic transformations, Probability Theory and Related Fields, 69 (1985), 461-478.doi: 10.1007/BF00532744. |
[19] |
G. Keller and C. Liverani, Stability of the spectrum for transfer operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28 (1999), 141-152. |
[20] |
C. Liverani, Invariant measures and their properties. A functional analytic point of view, Dynamical Systems. Part II, 185-237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, (2003). |
[21] |
C. Liverani, Multidimensional expanding maps with singularities: A pedestrian approach, Ergodic Theory and Dynamical Systems, 33 (2013), 168-182.doi: 10.1017/S0143385711000939. |
[22] |
C. Liverani, On contact Anosov flows, Ann. of Math. (2), 159 (2004), 1275-1312.doi: 10.4007/annals.2004.159.1275. |
[23] |
B. Saussol, Absolutely continuous invariant measures for multidimensional expanding maps, Israel J. Math., 116 (2000), 223-248.doi: 10.1007/BF02773219. |
[24] |
M. Rychlik, Bounded variation and invariant measures, Studia Math., 76 (1983), 69-80. |
[25] |
D. Thomine, A spectral gap for transfer operators of piecewise expanding maps, Discrete Contin. Dyn. Syst., 30 (2011), 917-944.doi: 10.3934/dcds.2011.30.917. |
[26] |
T. Masato, Quasi-compactness of transfer operators for contact Anosov flows, Nonlinearity, 23 (2010), 1495-1545.doi: 10.1088/0951-7715/23/7/001. |
[27] |
Z. Roger, Integration of Hölder forms and currents in snowflake spaces, Calc. Var. Partial Differential Equations, 40 (2011), 99-124.doi: 10.1007/s00526-010-0335-1. |