Normal forms and Sternberg conjugation theorems for infinite dimensional coupled map lattices

TL;DR

This paper establishes local Sternberg conjugation theorems for infinite-dimensional coupled map lattices with spatially decaying interactions, providing polynomial normal forms in resonant cases that preserve decay properties.

Contribution

It extends Sternberg conjugation theorems to infinite-dimensional lattice systems with non-finite range interactions, including resonant cases with polynomial normal forms.

Findings

Conjugations preserve spatial decay properties.

Normal forms are polynomial in resonant cases.

Applicable to infinite-dimensional lattice systems.

Abstract

In this paper we present local Sternberg conjugation theorems near attracting fixed points for lattice systems. The interactions are spatially decaying and are not restricted to finite distance. The conjugations obtained retain the same spatial decay. In the presence of resonances the conjugations are to a polynomial normal form that also has decaying properties.