Fast iteration of cocyles over rotations and Computation of hyperbolic bundles

Gemma Huguet (1) , Rafael de La Llave (2) , Yannick Sire (3)

1 CIMS - Courant Institute of Mathematical Sciences [New York]
2 School of Mathematics - Georgia Institute of Technology
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: quasi-periodic solutions; quasi-periodic cocycles; numerical computation

Domaines: Systèmes dynamiques [math.DS]

Gemma Huguet, Rafael de La Llave, Yannick Sire. Fast iteration of cocyles over rotations and Computation of hyperbolic bundles. Discrete and Continuous Dynamical Systems - Series A, 2013, 2013, pp.323--333. ⟨10.3934/proc.2013.2013.323⟩. ⟨hal-01338870⟩