Fast iteration of cocyles over rotations and Computation of hyperbolic bundles

TL;DR

This paper introduces efficient numerical algorithms for iterating hyperbolic cocycles over rotations and computing invariant bundles, facilitating the analysis of quasi-periodic dynamical systems and invariant structures.

Contribution

It presents novel fast algorithms that require minimal storage and operations for hyperbolic cocycle iteration and invariant bundle computation over rotations.

Findings

Algorithms are computationally efficient and require low storage.

Successfully compute hyperbolic cocycles and invariant bundles.

Enable further analysis of invariant tori in dynamical systems.

Abstract

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of hyperbolic cocycles over a rotation. We present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori.