Computation of Domains of analyticity of lower dimensional tori in a weakly dissipative Froeschl\'e map

TL;DR

This paper investigates how weak dissipation affects the analyticity domains of lower dimensional tori in a Froeschle9 map, providing formal expansions and supporting existing conjectures.

Contribution

It introduces a method to compute formal expansions of lower dimensional tori in both conservative and dissipative cases, estimating their analyticity domains as functions of perturbation.

Findings

Estimates of the shape of analyticity domains as functions of b5psilon.

Support for existing conjectures on the structure of these domains.

Formal expansions applicable to weakly dissipative systems.

Abstract

We consider a Froeschl\'e map and we add a weak dissipation of the form $\lambda(\varepsilon) = 1- \varepsilon^3$, where $\varepsilon$ is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the conservative and weakly dissipatives cases, and use them to estimate the shape of their domains of analyticity as functions of $\varepsilon$. Our results support conjectures in the literature.