Abstract:
We investigate transverse Hölder regularity of some canonical leaf conjugacies in normally hyperbolic dynamical systems and transverse Hölder regularity of some invariant foliations. Our results validate claims made elsewhere in the literature. © 2012 AIMSCIENCES.
Registro:
Documento: |
Artículo
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Título: | Hölder foliations, revisited |
Autor: | Pugh, C.; Shub, M.; Wilkinson, A. |
Filiación: | Department of Mathematics, University of Chicago, 5734 S. University Ave, Chicago, IL 60637, United States Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720, United States CONICET, IMAS, Universidad de Buenos Aires, Buenos Aires, Argentina Department of Mathematics, The CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, United States
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Palabras clave: | Hölder regularity of foliations; Invariant foliations; Normal hyperbolicity; Partial hyperbolicity |
Año: | 2012
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Volumen: | 6
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Número: | 1
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Página de inicio: | 79
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Página de fin: | 120
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DOI: |
http://dx.doi.org/10.3934/jmd.2012.6.79 |
Título revista: | Journal of Modern Dynamics
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Título revista abreviado: | J. Mod. Dyn.
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ISSN: | 19305311
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19305311_v6_n1_p79_Pugh |
Referencias:
- Anosov, D.V., Geodesic flows on closed Riemann manifolds with negative curvature, (Russian) (1967) Trudy Mat. Inst. Stecklov, 90, p. 209
- Bohnet, D., (2011) Partially Hyperbolic Systems With a Compact Center Foliation With Finite Holonomy, , Ph.D Thesis, Universität Hamburg
- Bonatti, C., Wilkinson, A., Transitive partially hyperbolic diffeomorphisms on 3-manifolds (2005) Topology, 44, pp. 475-508
- Burns, K., Wilkinson, A., Dynamical coherence and center bunching (2008) Discrete Contin. Dyn. Syst, 22, pp. 89-100
- Carrasco, P., (2010) Compact Dynamical Foliations, , Ph.D Thesis, University of Toronto, Canada
- Cheeger, J., Ebin, D., Comparison Theorems in Riemannian Geometry (1975) North-Holland Mathematical Library, 9. , North Holland Publishing Co., Amsterdam-Oxford, American Elsevier Publishing, Co., Inc., New York
- Chillingworth, D., (1970), unpublished, circa; Damjanovíc, D., Katok, A., Periodic cycle functionals and cocycle rigidity for certain partially hyperbolic Rk actions (2005) Discrete Contin. Dyn. Syst, 13, pp. 985-1005
- Damjanovíc, D., Katok, A., Local rigidity of partially hyperbolic actions. II. The geometric method and restrictions of Weyl chamber flows on SL(n,R)/Gamma (2011) Int. Math. Res. Not. IMRN, pp. 4405-4430
- Epstein, D., Foliations with all leaves compact (1976) Ann. Inst. Fourier (Grenoble), 26, pp. 265-282
- Hammerlindl, A., Quasi-isometry and plaque expansiveness (2011) Canadian Mathematical Bulletin, 54, pp. 676-679
- Hasselblatt, B., Regularity of the Anosov splitting. II (1997) Ergodic Theory Dynam. Systems, 17, pp. 169-172
- Hasselblatt, B., Wilkinson, A., Prevalence of non-Lipschitz Anosov foliations (1999) Ergodic Theory Dynam. Systems, 19, pp. 643-656
- Rodriguez, H.F., Rodriguez, H.M.A., Ures, R., A survey of partially hyperbolic dynamics (2007) Partially Hyperbolic Dynamics, Laminations, and Teichmüller Flow, 51, pp. 35-87. , Fields Inst. Commun, Amer. Math. Soc., Providence, RI
- Hirsch, M., Pugh, C., Shub, M., Invariant Manifolds (1977) Lecture Notes In Mathematics, 583. , Springer-Verlag, Berlin-New York
- Ilyashenko, Y., Negut, A., Hölder Properties of Perturbed Skew Products and Fubini Regained, , preprint
- Katok, A., Hasselblatt, B., Introduction to the Modern Theory of Dynamical Systems (1995) With a Supplementary Chapter By Katok and Leonardo Mendoza, Encyclopedia of Mathematics and Its Applications, 54. , Cambridge University Press, Cambridge
- Ni̧tiča, V., Török, A., Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices (1995) Duke Math. J, 79, pp. 751-810
- Pugh, C., Shub, M., Wilkinson, A., Hölder foliations (1997) Duke Math. J, 86, pp. 517-546
- Pugh, C., Shub, M., Wilkinson, A., Correction to: "Hölder foliations (2000) Duke Math. J, 105, pp. 105-106
- Schmeling, J., Siegmund-Schultze, R., (1992) Hölder-continuity of the Holonomy Maps For Hyperbolic Sets, 1514, pp. 174-191. , Springer, Berlin
- Shub, M., (1987) Global Stability of Dynamical Systems, , With the collaboration of Albert Fathi and Rémi Langevin, Translated from the French by Joseph Christy, Springer-Verlag, New York
- Wilkinson, A., Stable ergodicity of the time-one map of a geodesic flow (1998) Ergod. Th. & Dynam. Sys, 18, pp. 1545-1587
- Wilkinson, A., (2008) The Cohomological Equation For Partially Hyperbolic Diffeomorphisms, , preprint
Citas:
---------- APA ----------
Pugh, C., Shub, M. & Wilkinson, A.
(2012)
. Hölder foliations, revisited. Journal of Modern Dynamics, 6(1), 79-120.
http://dx.doi.org/10.3934/jmd.2012.6.79---------- CHICAGO ----------
Pugh, C., Shub, M., Wilkinson, A.
"Hölder foliations, revisited"
. Journal of Modern Dynamics 6, no. 1
(2012) : 79-120.
http://dx.doi.org/10.3934/jmd.2012.6.79---------- MLA ----------
Pugh, C., Shub, M., Wilkinson, A.
"Hölder foliations, revisited"
. Journal of Modern Dynamics, vol. 6, no. 1, 2012, pp. 79-120.
http://dx.doi.org/10.3934/jmd.2012.6.79---------- VANCOUVER ----------
Pugh, C., Shub, M., Wilkinson, A. Hölder foliations, revisited. J. Mod. Dyn. 2012;6(1):79-120.
http://dx.doi.org/10.3934/jmd.2012.6.79