Banach spaces for piecewise cone-hyperbolic maps

Journal of Modern Dynamics

Volumn 4, Issue 1, 2010, Pages 91-137

  Baladi, Viviane ^a   Gouëzel, Sébastien ^b  

^a ÉCOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

Anisotropic sobolev spaces; Exponential decay of correlations; Hyperbolic systems with singularities; Physical srb measures; Piecewise hyperbolic systems; Spectral gap; Transfer operators

Indexed keywords

EID: 77952184561     PISSN: 19305311     EISSN: None     Source Type: Journal    
DOI: 10.3934/jmd.2010.4.91     Document Type: Article

References (19)

1. ∞ foliations, Algebraic and topological dynamics, 123-135, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, (2005).
2. Viviane Baladi and Sébastien Gouëzel, Good Banach spaces for piecewise hyperbolic maps via interpolation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 1453-1481.
3. Michael Blank, Gerhard Keller and Carlangelo Liverani, Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity, 15 (2002), 1905-1973.
4. Viviane Baladi and David Ruelle, Sharp determinants, Invent. Math., 123 (1996), 553-574.
5. Viviane Baladi and Masato Tsujii, Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms, Ann. Inst. Fourier (Grenoble), 57 (2007), 127-154.
6. Viviane Baladi and Masato Tsujii, Dynamical determinants and spectrum for hyperbolic diffeomorphisms, Geometric and probabilistic structures in dynamics, 29-68, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, (2008).
7. Nikolai Chernov, Decay of correlations and dispersing billiards, J. Statist. Phys., 94 (1999), 513-556.
8. Nikolai Chernov, Astretchedexponentialboundontimecorrelationsforbilliardflows, J.Stat.Phys.,127 (2007), 21-50.
9. Mark F. Demers and Carlangelo Liverani, Stability of statistical properties in two-dimensional piecewise hyperbolic maps, Trans. Amer. Math. Soc., 360 (2008), 4777-4814.
10. Dmitry Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (2), 147 (1998), 357-390.
11. Sébastien Gouëzel and Carlangelo Liverani, Banach spaces adapted to Anosov systems, Ergodic Theory Dynam. Systems, 26 (2006), 189-217.
12. Sébastien Gouëzel and Carlangelo Liverani, Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties, J. Differential Geom., 79 (2008), 433-477.
13. Hubert Hennion, Sur un théorème spectral et son application aux noyaux lipchitziens, Proc. Amer. Math. Soc., 118 (1993), 627-634.
14. Boris Hasselblatt and Anatole Katok, Introduction to the modern theory of dynamical systems, With a supplementary chapter by Katok and Leonardo Mendoza, Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, Cambridge, 1995.
15. Morris W. Hirsch, Charles C. Pugh and Michael Shub, "Invariant Manifolds", Lecture Notes in Mathematics, Vol. 583, Springer-Verlag, Berlin-New York, 1977.
16. Carlangelo Liverani, On contact Anosov flows, Ann. of Math. (2), 159 (2004), 1275-1312.
17. Robert S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech., 16 (1967), 1031-1060.
18. Hans Triebel, General function spaces. III. Spaces B g (x) p,q and F g (x) p,q, 1
19. Lai-Sang Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math. (2), 147 (1998), 585-650.