Prevalence of non-Lipschitz Anosov foliations

Ergodic Theory and Dynamical Systems

Volumn 19, Issue 3, 1999, Pages 643-656

  Hasselblatt, Boris ^a   Wilkinson, Amie ^b  

^a TUFTS UNIVERSITY   (United States)

^b NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033465515     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385799133868     Document Type: Article

References (25)

1. D. V. Anosov. Geodesic flows on Riemann manifolds with negative curvature. Proc. Steklov Inst. 90 (1967).
2. D. V. Anosov. Tangent fields of transversal foliations in 'U-systems'. Math. Notes Acad. Sci. USSR 2(5) (1967), 818-823.
3. V. I. Arnol'd. Mathematical Methods of Classical Mechanics. Springer, Berlin, 1979.
4. L. Barreira. A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems. Ergod. Th. & Dynam. Sys. 16(5) (1996), 871-927.
5. Y. Benoist, P. Foulon and F. Labourie. Flots d'Anosov à distributions stable et instable différentiables. J. Amer. Math. Soc. 5(1) (1992), 33-74.
6. G. Besson, G. Courtois and S. Gallot. Minimal entropy and Mostow's rigidity theorems. Ergod. Th. & Dynam. Sys. 16(4) (1996), 623-649.
7. N. Fenichel. Asymptotic stability with rate conditions. Indiana University Math. J. 23 (1974), 1109-1137; 26(1) (1977), 81-93.
8. N. Fenichel. Asymptotic stability with rate conditions. Indiana University Math. J. 23 (1974), 1109-1137; 26(1) (1977), 81-93.
9. L. W. Green. The generalized geodesic flow. Duke Math. J. 41 (1974), 115-126.
10. M. Gerber and V. Niţicǎ. Hölder exponents of horocycle foliations on surfaces. Ergod. Th. & Dynam. Sys. to appear
11. M. Grayson, C. Pugh and M. Snub. Stably ergodic diffeomorphisms. Ann. Math. 140(2) (1994), 295-329.
12. B. Hasselblatt. Regularity of the Anosov splitting and of horospheric foliations. Ergod. Th. & Dynam. Sys. 14(4) (1994), 645-666.
13. B. Hasselblatt. Horospheric foliations and relative pinching. J. Diff. Geom. 39(1) (1994), 57-63.
14. B. Hasselblatt. Regularity of the Anosov splitting II. Ergod. Th. & Dynam. Sys. 17(1) (1997), 169-172.
15. M. Hirsch, C. Pugh and M. Shub. Invariant Manifolds (Lecture Notes in Mathematics, 583). Springer, 1977.
16. S. Hurder and A. Katok. Differentiability, rigidity, and Godbillon-Vey classes for Anosov flows. Publ. IHES 72 (1990), 5-61.
17. J.-L. Journé. A regularity lemma for functions of several variables. Revista Mat. Iberoamericana 4 (1988), 187-193.
18. M. Kanai. Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations. Ergod. Th. & Dynam. Sys. 8(2) (1988), 215-239.
19. A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1995.
20. F. Ledrappier and L.-S. Young. The metric entropy of diffeomorphisms, Part I: characterization of measures satisfying Pesin's entropy formula. Ann. Math. 122(3) (1985), 509-539.
21. R. de la Llave, J. M. Marco and R. Moriyon. Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation. Ann. Math. 123(3) (1986), 537-611.
22. C. Pugh and M. Shub. Stably ergodic dynamical systems and partial hyperbolicity. J. Complexity 13(1) (1997), 125-179.
23. C. Pugh, M. Shub and A. Wilkinson. Hölder foliations. Duke Math. J. 86(3) (1997), 517-546.
24. J. Schmeling and R. Siegmund-Schultze. Hölder continuity of the holonomy maps for hyperbolic basic sets. I. Ergodic Theory and Related Topics, III, Güstrow, 1990 (Lecture Notes in Mathematics, 1514). Springer, Berlin, 1992, pp. 174-191.
25. A. Wilkinson. Stable ergodicity of the time-one map of a geodesic flow. Ergod. Th. & Dynam. Sys. 18(6) (1998), 1545-1587.