Journal of Modern Dynamics (JMD)

Differentiable rigidity for quasiperiodic cocycles in compact Lie groups
Pages: 125 - 142, Volume 11, 2017

doi:10.3934/jmd.2017006      Abstract        References        Full text (223.8K)           Related Articles

Nikolaos Karaliolios - Imperial College London, South Kensington Campus, 180 Queen’s Gate, Huxley Building, London SW7 2AZ, United Kingdom (email)

1 A. Avila and R. Krikorian, Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles, Ann. of Math. (2), 164 (2006), 911-940.       
2 A. Avila, B. Fayad and R. Krikorian, A KAM scheme for $SL(2,\mathbbR)$ cocycles with Liouvillean frequencies, Geom. Funct. Anal., 21 (2011), 1001-1019.       
3 D. Bump, Lie Groups, Graduate Texts in Mathematics, 225, Springer-Verlag, New York, 2004.       
4 J. Dieudonné, Eléments d'Analyse, 5, Gauthier-Villars, 1975.
5 J. J. Duistermaat and J. A. C. Kolk, Lie Groups, Universitext, Springer-Verlag, Berlin, 2000.       
6 L. H. Eliasson, Ergodic skew-systems on $T^d \times SO(3,R)$, Ergodic Theory Dynam. Systems, 22 (2002), 1429-1449.       
7 B. Fayad and R. Krikorian, Rigidity results for quasiperiodic $SL(2,\mathbbR)$-cocycles, J. Mod. Dyn., 3 (2009), 497-510.       
8 H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math., 83 (1961), 573-601.       
9 S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962.
10 X. Hou and J. You, Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$, Discrete Contin. Dyn. Syst., 24 (2009), 441-454.       
11 N. Karaliolios, Invariant distributions for quasiperiodic cocycles in $\mathbbT^d \times SU(2)$, arXiv:1407.4763, 2014.
12 N. Karaliolios, Continuous spectrum or measurable reducibility for quasiperiodic cocycles in $\mathbbT ^d \times SU(2)$, arXiv:1512.00057, 2015.
13 N. Karaliolios, Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups, Mém. Soc. Math. Fr. (N.S.), No. 146 (2016), 4+ii+200 pp.       
14 A. Kolmogoroff, On inequalities between the upper bounds of the successive derivatives of an arbitrary function on an infinite interval, Amer. Math. Soc. Translation, 1949 (1949), 19 pp.       
15 R. Krikorian, Réductibilité des systèmes produits-croisés à valeurs dans des groupes compacts, Astérisque, (1999), vi+216 pp.       
16 R. Krikorian, Global density of reducible quasi-periodic cocycles on $T^1 \times SU(2)$, Ann. of Math. (2), 154 (2001), 269-326.       

Go to top