• Previous Article
    Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum
  • DCDS Home
  • This Issue
  • Next Article
    Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation
June  2009, 24(2): 441-454. doi: 10.3934/dcds.2009.24.441

Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$

1. 

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  March 2008 Revised  October 2008 Published  March 2009

In this paper, we consider the analytic reducibility problem of an analytic $d-$dimensional quasi-periodic cocycle $(\alpha,\ A)$ on $U(n)$ where $ \alpha$ is a Diophantine vector. We prove that, if the cocycle is conjugated to a constant cocycle $(\alpha,\ C)$ by a measurable conjugacy $(0,\ B)$, then for almost all $C$ it is analytically conjugated to $(\alpha,\ C)$ provided that $A$ is sufficiently close to some constant. Moreover $B$ is actually analytic if it is continuous.
Citation: Xuanji Hou, Jiangong You. Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 441-454. doi: 10.3934/dcds.2009.24.441
[1]

Xuanji Hou, Lei Jiao. On local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3125-3152. doi: 10.3934/dcds.2016.36.3125

[2]

Álvaro Castañeda, Gonzalo Robledo. Almost reducibility of linear difference systems from a spectral point of view. Communications on Pure & Applied Analysis, 2017, 16 (6) : 1977-1988. doi: 10.3934/cpaa.2017097

[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]

Dongfeng Zhang, Junxiang Xu, Xindong Xu. Reducibility of three dimensional skew symmetric system with Liouvillean basic frequencies. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2851-2877. doi: 10.3934/dcds.2018123

[5]

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

[6]

Claire Chavaudret, Stefano Marmi. Reducibility of quasiperiodic cocycles under a Brjuno-Rüssmann arithmetical condition. Journal of Modern Dynamics, 2012, 6 (1) : 59-78. doi: 10.3934/jmd.2012.6.59

[7]

Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Period doubling and reducibility in the quasi-periodically forced logistic map. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1507-1535. doi: 10.3934/dcdsb.2012.17.1507

[8]

Rafael de la Llave, Jason D. Mireles James. Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4321-4360. doi: 10.3934/dcds.2012.32.4321

[9]

Danijela Damjanovic and Anatole Katok. Local rigidity of actions of higher rank abelian groups and KAM method. Electronic Research Announcements, 2004, 10: 142-154.

[10]

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

[11]

Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Superstable periodic orbits of 1d maps under quasi-periodic forcing and reducibility loss. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 589-597. doi: 10.3934/dcds.2014.34.589

[12]

Wen Si, Fenfen Wang, Jianguo Si. Almost-periodic perturbations of non-hyperbolic equilibrium points via Pöschel-Rüssmann KAM method. Communications on Pure & Applied Analysis, 2020, 19 (1) : 541-585. doi: 10.3934/cpaa.2020027

[13]

Alessandra Celletti. Some KAM applications to Celestial Mechanics. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 533-544. doi: 10.3934/dcdss.2010.3.533

[14]

Dongfeng Yan. KAM Tori for generalized Benjamin-Ono equation. Communications on Pure & Applied Analysis, 2015, 14 (3) : 941-957. doi: 10.3934/cpaa.2015.14.941

[15]

Andrea Davini, Maxime Zavidovique. Weak KAM theory for nonregular commuting Hamiltonians. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 57-94. doi: 10.3934/dcdsb.2013.18.57

[16]

A. Kononenko. Twisted cocycles and rigidity problems. Electronic Research Announcements, 1995, 1: 26-34.

[17]

Jean Dolbeault, Maria J. Esteban, Gaspard Jankowiak. Onofri inequalities and rigidity results. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3059-3078. doi: 10.3934/dcds.2017131

[18]

Ilesanmi Adeboye, Harrison Bray, David Constantine. Entropy rigidity and Hilbert volume. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1731-1744. doi: 10.3934/dcds.2019075

[19]

Mads R. Bisgaard. Mather theory and symplectic rigidity. Journal of Modern Dynamics, 2019, 15: 165-207. doi: 10.3934/jmd.2019018

[20]

Michele V. Bartuccelli, G. Gentile, Kyriakos V. Georgiou. Kam theory, Lindstedt series and the stability of the upside-down pendulum. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 413-426. doi: 10.3934/dcds.2003.9.413

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]