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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), 1001-1019.
doi: 10.1007/s00039-011-0135-6. |
[2] |
A. D. Brjuno, An analytic form of differential equations, Math. Notes, 6 (1969), 927-931.
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), arXiv:0912.4814. |
[4] |
L. H. Eliasson, Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation, Comm. Math. Phys., 146 (1992), 447-482.
doi: 10.1007/BF02097013. |
[5] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems, in "Smooth Ergodic Theory and its Applications" (Seattle, WA, 1999), Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001), 679-705. |
[6] |
A. Giorgilli and S. Marmi, Convergence radius in the Poincaré-Siegel problem, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 601-621. |
[7] |
R. Johnson and J. Moser, The rotation number for almost periodic potentials, Comm. Math. Phys., 84 (1982), 403-438.
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), 265-293.
doi: 10.1007/s002200050110. |
[9] |
J. Pöschel, KAM à la R, Regul. Chaotic Dyn., 16 (2011), 17-23.
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), 683-718.
doi: 10.3934/dcdss.2010.3.683. |
[11] |
J.-C. Yoccoz, "Petits Diviseurs en Dimension 1", Astérisque, 231, Société mathématique de France, 1995. |
[12] |
L.-S. Young, Lyapunov exponents for some quasi-periodic cocycles, Ergodic Theory Dynam. Systems, 17 (1997), 483-504.
doi: 10.1017/S0143385797079170. |
[13] |
J. Wang and Q. Zhou, Reducibility results for quasiperiodic cocycles with Liouvillean frequency, J. Dynam. Differential Equations, 24 (2011), 61-83.
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), 1001-1019.
doi: 10.1007/s00039-011-0135-6. |
[2] |
A. D. Brjuno, An analytic form of differential equations, Math. Notes, 6 (1969), 927-931.
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), arXiv:0912.4814. |
[4] |
L. H. Eliasson, Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation, Comm. Math. Phys., 146 (1992), 447-482.
doi: 10.1007/BF02097013. |
[5] |
L. H. Eliasson, Almost reducibility of linear quasi-periodic systems, in "Smooth Ergodic Theory and its Applications" (Seattle, WA, 1999), Proc. Sympos. Pure Math., 69, Amer. Math. Soc., Providence, RI, (2001), 679-705. |
[6] |
A. Giorgilli and S. Marmi, Convergence radius in the Poincaré-Siegel problem, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 601-621. |
[7] |
R. Johnson and J. Moser, The rotation number for almost periodic potentials, Comm. Math. Phys., 84 (1982), 403-438.
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), 265-293.
doi: 10.1007/s002200050110. |
[9] |
J. Pöschel, KAM à la R, Regul. Chaotic Dyn., 16 (2011), 17-23.
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), 683-718.
doi: 10.3934/dcdss.2010.3.683. |
[11] |
J.-C. Yoccoz, "Petits Diviseurs en Dimension 1", Astérisque, 231, Société mathématique de France, 1995. |
[12] |
L.-S. Young, Lyapunov exponents for some quasi-periodic cocycles, Ergodic Theory Dynam. Systems, 17 (1997), 483-504.
doi: 10.1017/S0143385797079170. |
[13] |
J. Wang and Q. Zhou, Reducibility results for quasiperiodic cocycles with Liouvillean frequency, J. Dynam. Differential Equations, 24 (2011), 61-83.
doi: 10.1007/s10884-011-9235-0. |
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