The conjugacy theory

Abstract

In this chapter, we present precise formulations of the quasi-periodicity persistence theorems in the dissipative context, volume preserving context, Hamiltonian isotropic context and reversible context 1 (see Sections 1.3–1.4). The parameter μ labeling the vector fields is always assumed to vary in an open domain P ⊂ R^s, s ≥ 0. All the quantities δ _j , ε _j α _j , β _j are supposed to be real. The symbols $\mathcal{O}_d \left( a \right)$ denote a neighborhood of a point a in the Euclidean space R^d [we write $\mathcal{O}\left( a \right)$ instead of $\mathcal{O}_1 \left( a \right)$]. The letter Y denotes an open domain in R^d. Also, RP^d is the d-dimensional real projective space (d ∈ Z₊) and Π : R^d\ {0} → RP^d−1 for d ∈ N denotes the natural projection.