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Zygmund strong foliations in higher dimension
Lipschitz continuous invariant forms for algebraic Anosov systems
1. | Institut de Recherche Mathematique Avancée, UMR 7501 du Centre National de la Recherche Scientifique, 7 Rue René Descartes, 67084, Strasbourg Cedex, France |
2. | Department of Mathematics, Tufts University, Medford, MA 02155, United States |
Several features of the reasoning are interesting; namely, the use of exterior calculus for Lipschitz continuous forms, the arguments for geodesic flows and infranilmanifoldautomorphisms are quite different, and the need for mixing as opposed to ergodicity in the latter case.
References:
[1] |
Y. Benoist, P. Foulon and F. Labourie, Flots d'Anosov à distributions de Liapounov différentiables. I.,, Hyperbolic behaviour of dynamical systems (Paris, 53 (1990), 395.
|
[2] |
Y. Benoist, P. Foulon and F. Labourie, Flots d'Anosov à distributions stable et instable différentiables,, Journal of the American Mathematical Society, 5 (1992), 33.
|
[3] |
S. Dubrovskiy, Stokes Theorem for Lipschitz forms on a smooth manifold,, , (). Google Scholar |
[4] |
Y. Fang, On the rigidity of quasiconformal Anosov flows,, Ergodic Theory and Dynamical Systems, 27 (2007), 1773.
doi: doi:10.1017/S0143385707000326. |
[5] |
P. Foulon and B. Hasselblatt, Zygmund strong foliations,, Israel Journal of Mathematics, 138 (2003), 157.
doi: doi:10.1007/BF02783424. |
[6] |
Y. Fang, P. Foulon and B. Hasselblatt, Zygmund strong foliations in higher dimension,, Journal of Modern Dynamics, 4 (2010), 549. Google Scholar |
[7] |
V. M. Goldshtein, V. I. Kuzminov and I. A. Shvedov, Differential forms on a Lipschitz manifold,, Sibirsk. Mat. Zh., 23 (1982), 16.
|
[8] |
U. Hamenstädt, Invariant two-forms for geodesic flows,, Mathematische Annalen, 101 (1995), 677.
doi: doi:10.1007/BF01446654. |
[9] |
S. Hurder and A. Katok, Differentiability, rigidity, and Godbillon-Vey classes for Anosov flows,, Pub\-li\-ca\-tions Mathé\-ma\-tiques de l'Institut des Hautes \'Etudes Scientifiques, 72 (1990), 5.
doi: doi:10.1007/BF02699130. |
[10] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Encyclopedia of Mathematics and its Applications, 54 (1995).
|
[11] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry,", Interscience Publishers, (1963).
|
[12] |
W. F. Pfeffer, "Derivation and Integration,", Cambridge Tracts in Mathematics, (2001).
|
show all references
References:
[1] |
Y. Benoist, P. Foulon and F. Labourie, Flots d'Anosov à distributions de Liapounov différentiables. I.,, Hyperbolic behaviour of dynamical systems (Paris, 53 (1990), 395.
|
[2] |
Y. Benoist, P. Foulon and F. Labourie, Flots d'Anosov à distributions stable et instable différentiables,, Journal of the American Mathematical Society, 5 (1992), 33.
|
[3] |
S. Dubrovskiy, Stokes Theorem for Lipschitz forms on a smooth manifold,, , (). Google Scholar |
[4] |
Y. Fang, On the rigidity of quasiconformal Anosov flows,, Ergodic Theory and Dynamical Systems, 27 (2007), 1773.
doi: doi:10.1017/S0143385707000326. |
[5] |
P. Foulon and B. Hasselblatt, Zygmund strong foliations,, Israel Journal of Mathematics, 138 (2003), 157.
doi: doi:10.1007/BF02783424. |
[6] |
Y. Fang, P. Foulon and B. Hasselblatt, Zygmund strong foliations in higher dimension,, Journal of Modern Dynamics, 4 (2010), 549. Google Scholar |
[7] |
V. M. Goldshtein, V. I. Kuzminov and I. A. Shvedov, Differential forms on a Lipschitz manifold,, Sibirsk. Mat. Zh., 23 (1982), 16.
|
[8] |
U. Hamenstädt, Invariant two-forms for geodesic flows,, Mathematische Annalen, 101 (1995), 677.
doi: doi:10.1007/BF01446654. |
[9] |
S. Hurder and A. Katok, Differentiability, rigidity, and Godbillon-Vey classes for Anosov flows,, Pub\-li\-ca\-tions Mathé\-ma\-tiques de l'Institut des Hautes \'Etudes Scientifiques, 72 (1990), 5.
doi: doi:10.1007/BF02699130. |
[10] |
A. Katok and B. Hasselblatt, "Introduction to the Modern Theory of Dynamical Systems,", Encyclopedia of Mathematics and its Applications, 54 (1995).
|
[11] |
S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry,", Interscience Publishers, (1963).
|
[12] |
W. F. Pfeffer, "Derivation and Integration,", Cambridge Tracts in Mathematics, (2001).
|
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