-
Previous Article
Hölder foliations, revisited
- JMD Home
- This Issue
-
Next Article
On primes and period growth for Hamiltonian diffeomorphisms
Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition
1. | Département deMathématiques, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France |
2. | Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa (PI) |
References:
[1] |
A. Avila, B. Fayad and R. Krikorian, A KAM scheme for $SL(2,R)$ cocycles with Liouvillean frequencies,, Geom. Funct. Anal., 21 (2011), 1001.
doi: 10.1007/s00039-011-0135-6. |
[2] |
A. D. Brjuno, An analytic form of differential equations,, Math. Notes, 6 (1969), 927.
doi: 10.1007/BF01146416. |
[3] |
C. Chavaudret, Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles,, to appear in Bull. Soc. Math. France, (2010). Google Scholar |
[4] |
L. H. Eliasson, Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation,, Comm. Math. Phys., 146 (1992), 447.
doi: 10.1007/BF02097013. |
[5] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems,, in, 69 (2001), 679.
|
[6] |
A. Giorgilli and S. Marmi, Convergence radius in the Poincaré-Siegel problem,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 601.
|
[7] |
R. Johnson and J. Moser, The rotation number for almost periodic potentials,, Comm. Math. Phys., 84 (1982), 403.
doi: 10.1007/BF01208484. |
[8] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The Brjuno functions and their regularity properties,, Comm. Math. Phys., 186 (1997), 265.
doi: 10.1007/s002200050110. |
[9] |
J. Pöschel, KAM à la R,, Regul. Chaotic Dyn., 16 (2011), 17.
doi: 10.1134/S1560354710520060. |
[10] |
H. Rüssmann, KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 683.
doi: 10.3934/dcdss.2010.3.683. |
[11] |
J.-C. Yoccoz, "Petits Diviseurs en Dimension 1",, Astérisque, 231 (1995). Google Scholar |
[12] |
L.-S. Young, Lyapunov exponents for some quasi-periodic cocycles,, Ergodic Theory Dynam. Systems, 17 (1997), 483.
doi: 10.1017/S0143385797079170. |
[13] |
J. Wang and Q. Zhou, Reducibility results for quasiperiodic cocycles with Liouvillean frequency,, J. Dynam. Differential Equations, 24 (2011), 61.
doi: 10.1007/s10884-011-9235-0. |
show all references
References:
[1] |
A. Avila, B. Fayad and R. Krikorian, A KAM scheme for $SL(2,R)$ cocycles with Liouvillean frequencies,, Geom. Funct. Anal., 21 (2011), 1001.
doi: 10.1007/s00039-011-0135-6. |
[2] |
A. D. Brjuno, An analytic form of differential equations,, Math. Notes, 6 (1969), 927.
doi: 10.1007/BF01146416. |
[3] |
C. Chavaudret, Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles,, to appear in Bull. Soc. Math. France, (2010). Google Scholar |
[4] |
L. H. Eliasson, Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation,, Comm. Math. Phys., 146 (1992), 447.
doi: 10.1007/BF02097013. |
[5] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems,, in, 69 (2001), 679.
|
[6] |
A. Giorgilli and S. Marmi, Convergence radius in the Poincaré-Siegel problem,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 601.
|
[7] |
R. Johnson and J. Moser, The rotation number for almost periodic potentials,, Comm. Math. Phys., 84 (1982), 403.
doi: 10.1007/BF01208484. |
[8] |
S. Marmi, P. Moussa and J.-C. Yoccoz, The Brjuno functions and their regularity properties,, Comm. Math. Phys., 186 (1997), 265.
doi: 10.1007/s002200050110. |
[9] |
J. Pöschel, KAM à la R,, Regul. Chaotic Dyn., 16 (2011), 17.
doi: 10.1134/S1560354710520060. |
[10] |
H. Rüssmann, KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 683.
doi: 10.3934/dcdss.2010.3.683. |
[11] |
J.-C. Yoccoz, "Petits Diviseurs en Dimension 1",, Astérisque, 231 (1995). Google Scholar |
[12] |
L.-S. Young, Lyapunov exponents for some quasi-periodic cocycles,, Ergodic Theory Dynam. Systems, 17 (1997), 483.
doi: 10.1017/S0143385797079170. |
[13] |
J. Wang and Q. Zhou, Reducibility results for quasiperiodic cocycles with Liouvillean frequency,, J. Dynam. Differential Equations, 24 (2011), 61.
doi: 10.1007/s10884-011-9235-0. |
[1] |
Claire Chavaudret, Stefano Marmi. Erratum: Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition. Journal of Modern Dynamics, 2015, 9: 285-287. doi: 10.3934/jmd.2015.9.285 |
[2] |
João Lopes Dias. Brjuno condition and renormalization for Poincaré flows. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 641-656. doi: 10.3934/dcds.2006.15.641 |
[3] |
Hans Koch, João Lopes Dias. Renormalization of diophantine skew flows, with applications to the reducibility problem. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 477-500. doi: 10.3934/dcds.2008.21.477 |
[4] |
Percy A. Deift, Thomas Trogdon, Govind Menon. On the condition number of the critically-scaled Laguerre Unitary Ensemble. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4287-4347. doi: 10.3934/dcds.2016.36.4287 |
[5] |
Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007 |
[6] |
Saša Kocić. Reducibility of skew-product systems with multidimensional Brjuno base flows. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 261-283. doi: 10.3934/dcds.2011.29.261 |
[7] |
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander, James A. Yorke. Solving the Babylonian problem of quasiperiodic rotation rates. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : 2279-2305. doi: 10.3934/dcdss.2019145 |
[8] |
E. Muñoz Garcia, R. Pérez-Marco. Diophantine conditions in small divisors and transcendental number theory. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1401-1409. doi: 10.3934/dcds.2003.9.1401 |
[9] |
Masaru Ikehata. On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method. Inverse Problems & Imaging, 2017, 11 (1) : 99-123. doi: 10.3934/ipi.2017006 |
[10] |
Lan Zeng, Guoxi Ni, Yingying Li. Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5503-5522. doi: 10.3934/dcdsb.2019068 |
[11] |
Hongxiu Zhong, Guoliang Chen, Xueping Guo. Semi-local convergence of the Newton-HSS method under the center Lipschitz condition. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 85-99. doi: 10.3934/naco.2019007 |
[12] |
Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 |
[13] |
TÔn Vı$\underset{.}{\overset{\hat{\ }}{\mathop{\text{E}}}}\, $T T$\mathop {\text{A}}\limits_. $, Linhthi hoai Nguyen, Atsushi Yagi. A sustainability condition for stochastic forest model. Communications on Pure & Applied Analysis, 2017, 16 (2) : 699-718. doi: 10.3934/cpaa.2017034 |
[14] |
Baojun Bian, Pengfei Guan. A structural condition for microscopic convexity principle. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 789-807. doi: 10.3934/dcds.2010.28.789 |
[15] |
Shie Mannor, Vianney Perchet, Gilles Stoltz. A primal condition for approachability with partial monitoring. Journal of Dynamics & Games, 2014, 1 (3) : 447-469. doi: 10.3934/jdg.2014.1.447 |
[16] |
Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020184 |
[17] |
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020196 |
[18] |
Wenxian Shen. Global attractor and rotation number of a class of nonlinear noisy oscillators. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 597-611. doi: 10.3934/dcds.2007.18.597 |
[19] |
Danijela Damjanovic and Anatole Katok. Local rigidity of actions of higher rank abelian groups and KAM method. Electronic Research Announcements, 2004, 10: 142-154. |
[20] |
Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17 |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]