Fast iteration of cocycles over rotations and computation of hyperbolic bundles

Pages: 323 - 333, Issue special, November 2013

 Abstract        References        Full Text (788.9K)              

Gemma Huguet - Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States (email)
Rafael de la Llave - School of Mathematics, Georgia Institute of Technology, 686 Cherry St., Atlanta, GA 30332-0160, United States (email)
Yannick Sire - Université Paul Cézanne, Laboratoire LATP UMR 6632, Marseille, France (email)

Abstract: We present numerical algorithms that use small requirements of storage and operations to compute the iteration of cocycles over a rotation. We also show that these algorithms can be used to compute efficiently the stable and unstable bundles and the Lyapunov exponents of the cocycle.

Keywords:  Quasi-periodic solutions, quasi-periodic cocycles, numerical computation.
Mathematics Subject Classification:  Primary: 70K43; Secondary: 37J40.

Received: July 2012;      Revised: February 2013;      Published: November 2013.