-
Previous Article
The Khinchin Theorem for interval-exchange transformations
- JMD Home
- This Issue
-
Next Article
Counting closed geodesics in moduli space
Integrability and Lyapunov exponents
1. | Instituto Nacional deMatemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil |
References:
[1] |
D. V. Anosov, "Geodesic Flows on Closed Riemannian Manifolds with Negative Curvature,", Proceedings of the Steklov Institute of Mathematics, (1967).
|
[2] |
L. Barriera and C. Valls, Center manifolds for nonuniformly partially hyperbolic diffeomorphisms,, Journal de Mathématiques Pures et Appliquées, 84 (2005), 1693.
doi: 10.1016/j.matpur.2005.07.005. |
[3] |
M. Brin and Ja. Pesin, Partially hyperbolic dynamical systems,, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170.
|
[4] |
K. Burns, F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Talitskaya and R. Ures, Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center,, Discrete and Continuous Dynamical Systems, 22 (2008), 75.
doi: 10.3934/dcds.2008.22.75. |
[5] |
K. Burns and A. Wilkinson, Dynamical coherence and center bunching,, Discrete and Continuous Dynamical Systems, 22 (2008), 89.
doi: 10.3934/dcds.2008.22.89. |
[6] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems,, Annals of Math., 171 (2010), 451.
|
[7] |
X. Cabré, E. Fontich and R. de la Llave, The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces,, Indiana Univ. Math. J., 52 (2003), 283.
doi: 10.1512/iumj.2003.52.2245. |
[8] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, A survey of partially hyperbolic dynamics,, Partially Hyperbolic Dynamics, (2007), 35.
|
[9] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle,, Invent. Math., 172 (2008), 353.
doi: 10.1007/s00222-007-0100-z. |
[10] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," volume 583 of "Lecture Notes in Mathematics," Vol. 583,, Springer-Verlag, (1977).
|
[11] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,", Translated from the Portuguese by Silvio Levy. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], (1987).
|
[12] |
V. Oseledets, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 197.
|
[13] |
V. Oseledets, Oseledets theorem,, Scholarpedia, 3 (2008).
doi: 10.4249/scholarpedia.1846. |
[14] |
F. Rampazzo, Frobenius-type theorems for Lipschitz distributions,, Journal of Differential Equations, 243 (2007), 270.
doi: 10.1016/j.jde.2007.05.040. |
[15] |
S. Simić, Lipschitz distributions and Anosov flows,, Proc. of the Amer. Math. Soc., 124 (1996), 1869.
doi: 10.1090/S0002-9939-96-03423-5. |
[16] |
S. Smale, Differentiable dynamical systems,, Bull. Amer. Math. Soc., 73 (1967), 747.
doi: 10.1090/S0002-9904-1967-11798-1. |
[17] |
A. Wilkinson, Stable ergodicity of the time-one map of a geodesic flow,, Ergod. Th. and Dynam. Sys., 18 (1998), 1545.
doi: 10.1017/S0143385798117984. |
show all references
References:
[1] |
D. V. Anosov, "Geodesic Flows on Closed Riemannian Manifolds with Negative Curvature,", Proceedings of the Steklov Institute of Mathematics, (1967).
|
[2] |
L. Barriera and C. Valls, Center manifolds for nonuniformly partially hyperbolic diffeomorphisms,, Journal de Mathématiques Pures et Appliquées, 84 (2005), 1693.
doi: 10.1016/j.matpur.2005.07.005. |
[3] |
M. Brin and Ja. Pesin, Partially hyperbolic dynamical systems,, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 38 (1974), 170.
|
[4] |
K. Burns, F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Talitskaya and R. Ures, Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center,, Discrete and Continuous Dynamical Systems, 22 (2008), 75.
doi: 10.3934/dcds.2008.22.75. |
[5] |
K. Burns and A. Wilkinson, Dynamical coherence and center bunching,, Discrete and Continuous Dynamical Systems, 22 (2008), 89.
doi: 10.3934/dcds.2008.22.89. |
[6] |
K. Burns and A. Wilkinson, On the ergodicity of partially hyperbolic systems,, Annals of Math., 171 (2010), 451.
|
[7] |
X. Cabré, E. Fontich and R. de la Llave, The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces,, Indiana Univ. Math. J., 52 (2003), 283.
doi: 10.1512/iumj.2003.52.2245. |
[8] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, A survey of partially hyperbolic dynamics,, Partially Hyperbolic Dynamics, (2007), 35.
|
[9] |
F. Rodriguez Hertz, M. A. Rodriguez Hertz and R. Ures, Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1D-center bundle,, Invent. Math., 172 (2008), 353.
doi: 10.1007/s00222-007-0100-z. |
[10] |
M. Hirsch, C. Pugh and M. Shub, "Invariant Manifolds," volume 583 of "Lecture Notes in Mathematics," Vol. 583,, Springer-Verlag, (1977).
|
[11] |
R. Mañé, "Ergodic Theory and Differentiable Dynamics,", Translated from the Portuguese by Silvio Levy. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], (1987).
|
[12] |
V. Oseledets, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems,, Trans. Moscow Math. Soc., 19 (1968), 197.
|
[13] |
V. Oseledets, Oseledets theorem,, Scholarpedia, 3 (2008).
doi: 10.4249/scholarpedia.1846. |
[14] |
F. Rampazzo, Frobenius-type theorems for Lipschitz distributions,, Journal of Differential Equations, 243 (2007), 270.
doi: 10.1016/j.jde.2007.05.040. |
[15] |
S. Simić, Lipschitz distributions and Anosov flows,, Proc. of the Amer. Math. Soc., 124 (1996), 1869.
doi: 10.1090/S0002-9939-96-03423-5. |
[16] |
S. Smale, Differentiable dynamical systems,, Bull. Amer. Math. Soc., 73 (1967), 747.
doi: 10.1090/S0002-9904-1967-11798-1. |
[17] |
A. Wilkinson, Stable ergodicity of the time-one map of a geodesic flow,, Ergod. Th. and Dynam. Sys., 18 (1998), 1545.
doi: 10.1017/S0143385798117984. |
[1] |
Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020 doi: 10.3934/jcd.2021006 |
[2] |
Peter Giesl, Sigurdur Hafstein. System specific triangulations for the construction of CPA Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020378 |
[3] |
Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 299-336. doi: 10.3934/dcdsb.2020331 |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]