Partial preservation of frequencies and Floquet exponents of invariant tori in the reversible KAM context 2

TL;DR

This paper investigates the persistence of invariant tori in reversible KAM theory, demonstrating partial preservation of frequencies and Floquet exponents under weak nondegeneracy conditions using Herman's method.

Contribution

It introduces new nondegeneracy conditions ensuring the preservation of specific frequencies and Floquet exponents in reversible KAM context 2.

Findings

Partial preservation of frequencies in invariant tori.

Partial preservation of Floquet exponents.

Persistence results under weak nondegeneracy conditions.

Abstract

We consider the persistence of smooth families of invariant tori in the reversible context 2 of KAM theory under various weak nondegeneracy conditions via Herman's method. The reversible KAM context 2 refers to the situation where the dimension of the fixed point manifold of the reversing involution is less than half the codimension of the invariant torus in question. The nondegeneracy conditions we employ ensure the preservation of any prescribed subsets of the frequencies of the unperturbed tori and of their Floquet exponents (the eigenvalues of the coefficient matrix of the variational equation along the torus).