Linearization of multi-frequency quasi-periodically forced circle flows beyond Brjuno condition

Abstract

In this article, we considered the linearization of analytic quasi-periodically forced circle flows. We generalized the rotational linearization of systems with two-dimensional base frequency to systems with any finite dimensional base frequency case. Meanwhile, we relaxed the arithmetical limitations on the base frequencies. Our proof is based on a generalized Kolmogorov–Arnold–Moser (KAM) scheme.

Keywords

• linearization
• quasi-periodically forced circle flow
• liouvillean frequency