Equivariant nonautonomous normal forms
type: Item
instance of: scholarly article
title: Equivariant nonautonomous normal forms
zbMATH Open document ID: 1475.37055
author: Luís Barreira
author: Claudia Valls
published in: Qualitative Theory of Dynamical Systems
publication date: 2021-09-07T00:00:00Z
review text: For a nonautonomous dynamics with discrete time, the authors show that if the dynamics is equivariant (respectively, reversible), then any normal form, as well as the coordinate change bringing the dynamics into this normal form, have equivariance (respectively, reversibility) properties. They consider dynamics on \(\mathbb{R}^d\) given by \(x_{n+1}=A_nx_n+f_n(x_n)\), where the \(d\times d\)-matrices \(A_n\) are invertible and the maps \(f_n\) are of class \(C^p\), \(p\in \mathbb{N}\). The authors study the relationship between the nonuniform spectrum, the block decomposition of the matrices \(A_n\), the resonances and an explicit construction of the coordinate change which gives the normal form.
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37G40
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 39A30
zbMATH DE Number: 7391779
zbMATH Keywords: nonuniform hyperbolicity
zbMATH Keywords: spectrum
zbMATH Keywords: normal forms
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: s12346-021-00513-6
OpenAlex ID: W3196121485
cites work: Q5431024
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cites work: Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
cites work: A spectral theory for linear differential systems
cites work: Reversible systems
DOI: 10.1007/S12346-021-00513-6
description: scientific article; zbMATH DE number 7391779