-
Previous Article
Lipschitz continuous invariant forms for algebraic Anosov systems
- JMD Home
- This Issue
-
Next Article
Nonexpanding attractors: Conjugacy to algebraic models and classification in 3-manifolds
Zygmund strong foliations in higher dimension
1. | Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302, Cergy-Pontoise Cedex, France |
2. | Institut de Recherche Mathematique Avancée, UMR 7501 du Centre National de la Recherche Scientifique, 7 Rue René Descartes, 67084, Strasbourg Cedex |
3. | Department of Mathematics, Tufts University, Medford, MA 02155 |
References:
[1] |
N. Dairbekov and G. Paternain, Longitudinal KAM cocycles and action spectra of magnetic flows, Mathematics Research Letters, 12 (2005), 719-729. |
[2] |
D. DeLatte, Nonstationary normal forms and cocycle invariants, Random and Computational Dynamics, 1 (1992/93), 229-259; On normal forms in Hamiltonian dynamics, a new approach to some convergence questions, Ergodic Theory and Dynamical Systems, 15 (1995), 49-66. |
[3] |
Y. Fang, On the rigidity of quasiconformal Anosov flows, Ergodic Theory and Dynamical Systems, 27 (2007), 1773-1802.
doi: doi:10.1017/S0143385707000326. |
[4] |
Y. Fang, Smooth rigidity of quasiconformal Anosov flows, Ergodic Theory and Dynamical Systems, 24 (2004), 1937-1959.
doi: doi:10.1017/S0143385704000264. |
[5] |
Y. Fang, Thermodynamic invariants of Anosov flows and rigidity, Discrete Contin. Dyn. Syst., 24 (2009), 1185-1204.
doi: doi:10.3934/dcds.2009.24.1185. |
[6] |
R. Feres and A. Katok, Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory and Dynamical Systems, 9 (1989), 427-432.
doi: doi:10.1017/S0143385700005071. |
[7] |
P. Foulon and B. Hasselblatt, Zygmund strong foliations, Israel Journal of Mathematics, 138 (2003), 157-188.
doi: doi:10.1007/BF02783424. |
[8] |
P. Foulon and B. Hasselblatt, Lipschitz continuous invariant forms for algebraic Anosov systems, Journal of Modern Dynamics, 4 (2010), 571-584. |
[9] |
M. Guysinsky, The theory of nonstationary normal forms, Ergod. Theory and Dyn. Syst., 22 (2002), 845-862.
doi: doi:10.1017/S0143385702000421. |
[10] |
M. Guysinsky and A. Katok, Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations, Math. Research Letters, 5 (1998), 149-163. |
[11] |
J. S. Hadamard, Sur l'itération et les solutions asymptotiques des équations différentielles, Bulletin de la Société Mathématique de France, 29 (1901), 224-228. |
[12] |
B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory and Dynamical Systems, 14 (1994), 645-666. |
[13] |
U. Hamenstädt, Invariant two-forms for geodesic flows, Mathematische Annalen, 101 (1995), 677-698.
doi: doi:10.1007/BF01446654. |
[14] |
B. Hasselblatt, Hyperbolic dynamics, in "Handbook of Dynamical Systems," 1A, North Holland, (2002), 239-319. |
[15] |
S. Hurder and A. Katok, Differentiability, rigidity, and Godbillon-Vey classes for Anosov flows, Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 72 (1990), 5-61.
doi: doi:10.1007/BF02699130. |
[16] |
M. Kanai, Differential-geometric studies on dynamics of geodesic and frame flows, Japan. J. Math., 19 (1993), 1-30. |
[17] |
A. Katok and B. Hasselblatt, "Introduction To The Modern Theory Of Dynamical Systems," Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, 1995. |
[18] |
A. Katok and J. Lewis, Local rigidity for certain groups of toral automorphisms, Israel J. Math., 75 (1991), 203-241. |
[19] |
R. de la Llave and R. Obaya, Regularity of the composition operator in spaces of Hölder functions, Discrete Contin. Dynam. Systems, 5 (1999), 157-184. |
[20] |
G. P. Paternain, The longitudinal KAM-cocycle of a magnetic flow, Math. Proc. Cambridge Philos. Soc., 139 (2005), 307-316.
doi: doi:10.1017/S0305004105008613. |
[21] |
G. Paternain, On two noteworthy deformations of negatively curved Riemannian metrics, Discrete Contin. Dynam. Systems, 5 (1999), 639-650.
doi: doi:10.3934/dcds.1999.5.639. |
[22] |
G. Paternain and W. J. Merry, Stability of Anosov Hamiltonian structures, arXiv:0903.3969. |
[23] |
V. Sadovskaya, On uniformly quasiconformal Anosov systems, Mathematical Research Letters, 12 (2005), 425-441. |
[24] |
C. Yue, Quasiconformality in the geodesic flow of negatively curved manifolds, Geom. Funct. Anal., 6 (1996), 740-750.
doi: doi:10.1007/BF02247120. |
[25] |
A. S. Zygmund, "Trigonometric Series," Cambridge University Press, 1959 (and 1968, 1979, 1988), revised version of "Trigonometrical Series," Monografje Matematyczne, Tom V., Warszawa-Lwow, 1935. |
show all references
References:
[1] |
N. Dairbekov and G. Paternain, Longitudinal KAM cocycles and action spectra of magnetic flows, Mathematics Research Letters, 12 (2005), 719-729. |
[2] |
D. DeLatte, Nonstationary normal forms and cocycle invariants, Random and Computational Dynamics, 1 (1992/93), 229-259; On normal forms in Hamiltonian dynamics, a new approach to some convergence questions, Ergodic Theory and Dynamical Systems, 15 (1995), 49-66. |
[3] |
Y. Fang, On the rigidity of quasiconformal Anosov flows, Ergodic Theory and Dynamical Systems, 27 (2007), 1773-1802.
doi: doi:10.1017/S0143385707000326. |
[4] |
Y. Fang, Smooth rigidity of quasiconformal Anosov flows, Ergodic Theory and Dynamical Systems, 24 (2004), 1937-1959.
doi: doi:10.1017/S0143385704000264. |
[5] |
Y. Fang, Thermodynamic invariants of Anosov flows and rigidity, Discrete Contin. Dyn. Syst., 24 (2009), 1185-1204.
doi: doi:10.3934/dcds.2009.24.1185. |
[6] |
R. Feres and A. Katok, Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory and Dynamical Systems, 9 (1989), 427-432.
doi: doi:10.1017/S0143385700005071. |
[7] |
P. Foulon and B. Hasselblatt, Zygmund strong foliations, Israel Journal of Mathematics, 138 (2003), 157-188.
doi: doi:10.1007/BF02783424. |
[8] |
P. Foulon and B. Hasselblatt, Lipschitz continuous invariant forms for algebraic Anosov systems, Journal of Modern Dynamics, 4 (2010), 571-584. |
[9] |
M. Guysinsky, The theory of nonstationary normal forms, Ergod. Theory and Dyn. Syst., 22 (2002), 845-862.
doi: doi:10.1017/S0143385702000421. |
[10] |
M. Guysinsky and A. Katok, Normal forms and invariant geometric structures for dynamical systems with invariant contracting foliations, Math. Research Letters, 5 (1998), 149-163. |
[11] |
J. S. Hadamard, Sur l'itération et les solutions asymptotiques des équations différentielles, Bulletin de la Société Mathématique de France, 29 (1901), 224-228. |
[12] |
B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory and Dynamical Systems, 14 (1994), 645-666. |
[13] |
U. Hamenstädt, Invariant two-forms for geodesic flows, Mathematische Annalen, 101 (1995), 677-698.
doi: doi:10.1007/BF01446654. |
[14] |
B. Hasselblatt, Hyperbolic dynamics, in "Handbook of Dynamical Systems," 1A, North Holland, (2002), 239-319. |
[15] |
S. Hurder and A. Katok, Differentiability, rigidity, and Godbillon-Vey classes for Anosov flows, Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 72 (1990), 5-61.
doi: doi:10.1007/BF02699130. |
[16] |
M. Kanai, Differential-geometric studies on dynamics of geodesic and frame flows, Japan. J. Math., 19 (1993), 1-30. |
[17] |
A. Katok and B. Hasselblatt, "Introduction To The Modern Theory Of Dynamical Systems," Encyclopedia of Mathematics and its Applications, 54, Cambridge University Press, 1995. |
[18] |
A. Katok and J. Lewis, Local rigidity for certain groups of toral automorphisms, Israel J. Math., 75 (1991), 203-241. |
[19] |
R. de la Llave and R. Obaya, Regularity of the composition operator in spaces of Hölder functions, Discrete Contin. Dynam. Systems, 5 (1999), 157-184. |
[20] |
G. P. Paternain, The longitudinal KAM-cocycle of a magnetic flow, Math. Proc. Cambridge Philos. Soc., 139 (2005), 307-316.
doi: doi:10.1017/S0305004105008613. |
[21] |
G. Paternain, On two noteworthy deformations of negatively curved Riemannian metrics, Discrete Contin. Dynam. Systems, 5 (1999), 639-650.
doi: doi:10.3934/dcds.1999.5.639. |
[22] |
G. Paternain and W. J. Merry, Stability of Anosov Hamiltonian structures, arXiv:0903.3969. |
[23] |
V. Sadovskaya, On uniformly quasiconformal Anosov systems, Mathematical Research Letters, 12 (2005), 425-441. |
[24] |
C. Yue, Quasiconformality in the geodesic flow of negatively curved manifolds, Geom. Funct. Anal., 6 (1996), 740-750.
doi: doi:10.1007/BF02247120. |
[25] |
A. S. Zygmund, "Trigonometric Series," Cambridge University Press, 1959 (and 1968, 1979, 1988), revised version of "Trigonometrical Series," Monografje Matematyczne, Tom V., Warszawa-Lwow, 1935. |
[1] |
Yong Fang. Quasiconformal Anosov flows and quasisymmetric rigidity of Hamenst$\ddot{a}$dt distances. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3471-3483. doi: 10.3934/dcds.2014.34.3471 |
[2] |
Yong Fang. Thermodynamic invariants of Anosov flows and rigidity. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1185-1204. doi: 10.3934/dcds.2009.24.1185 |
[3] |
Boris Hasselblatt. Critical regularity of invariant foliations. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 931-937. doi: 10.3934/dcds.2002.8.931 |
[4] |
Yong Fang. Rigidity of Hamenstädt metrics of Anosov flows. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1271-1278. doi: 10.3934/dcds.2016.36.1271 |
[5] |
Yong Fang, Patrick Foulon, Boris Hasselblatt. Longitudinal foliation rigidity and Lipschitz-continuous invariant forms for hyperbolic flows. Electronic Research Announcements, 2010, 17: 80-89. doi: 10.3934/era.2010.17.80 |
[6] |
Boris Kalinin, Anatole Katok. Measure rigidity beyond uniform hyperbolicity: invariant measures for cartan actions on tori. Journal of Modern Dynamics, 2007, 1 (1) : 123-146. doi: 10.3934/jmd.2007.1.123 |
[7] |
Rafael De La Llave, Victoria Sadovskaya. On the regularity of integrable conformal structures invariant under Anosov systems. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 377-385. doi: 10.3934/dcds.2005.12.377 |
[8] |
Changguang Dong, Adam Kanigowski. Rigidity of a class of smooth singular flows on $ \mathbb{T}^2 $. Journal of Modern Dynamics, 2020, 16: 37-57. doi: 10.3934/jmd.2020002 |
[9] |
Hua Qiu. Regularity criteria of smooth solution to the incompressible viscoelastic flow. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2873-2888. doi: 10.3934/cpaa.2013.12.2873 |
[10] |
Ilesanmi Adeboye, Harrison Bray, David Constantine. Entropy rigidity and Hilbert volume. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1731-1744. doi: 10.3934/dcds.2019075 |
[11] |
Woochul Jung, Keonhee Lee, Carlos Morales, Jumi Oh. Rigidity of random group actions. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6845-6854. doi: 10.3934/dcds.2020130 |
[12] |
Jean Dolbeault, Maria J. Esteban, Gaspard Jankowiak. Onofri inequalities and rigidity results. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3059-3078. doi: 10.3934/dcds.2017131 |
[13] |
A. Kononenko. Twisted cocycles and rigidity problems. Electronic Research Announcements, 1995, 1: 26-34. |
[14] |
Mads R. Bisgaard. Mather theory and symplectic rigidity. Journal of Modern Dynamics, 2019, 15: 165-207. doi: 10.3934/jmd.2019018 |
[15] |
Boris Kalinin, Anatole Katok, Federico Rodriguez Hertz. Errata to "Measure rigidity beyond uniform hyperbolicity: Invariant measures for Cartan actions on tori" and "Uniqueness of large invariant measures for $\Zk$ actions with Cartan homotopy data". Journal of Modern Dynamics, 2010, 4 (1) : 207-209. doi: 10.3934/jmd.2010.4.207 |
[16] |
David Constantine. 2-Frame flow dynamics and hyperbolic rank-rigidity in nonpositive curvature. Journal of Modern Dynamics, 2008, 2 (4) : 719-740. doi: 10.3934/jmd.2008.2.719 |
[17] |
Boris Hasselblatt and Amie Wilkinson. Prevalence of non-Lipschitz Anosov foliations. Electronic Research Announcements, 1997, 3: 93-98. |
[18] |
Plamen Stefanov and Gunther Uhlmann. Recent progress on the boundary rigidity problem. Electronic Research Announcements, 2005, 11: 64-70. |
[19] |
Zhenqi Jenny Wang. Local rigidity of partially hyperbolic actions. Journal of Modern Dynamics, 2010, 4 (2) : 271-327. doi: 10.3934/jmd.2010.4.271 |
[20] |
Zhenqi Jenny Wang. Local rigidity of partially hyperbolic actions. Electronic Research Announcements, 2010, 17: 68-79. doi: 10.3934/era.2010.17.68 |
2021 Impact Factor: 0.641
Tools
Metrics
Other articles
by authors
[Back to Top]