Normal forms for difference and differential systems
type: Item
instance of: scholarly article
title: Normal forms for difference and differential systems
zbMATH Open document ID: 1500.37039
author: Meijia Liu
author: Hao Wu
author: Zhihua Ren
published in: Qualitative Theory of Dynamical Systems
publication date: 2022-03-15T00:00:00Z
review text: There are two ways to bridge difference and differential equations. One is the suspension, which makes diffeomorphisms as Poincaré recurrence maps of periodic differential systems. The second is the Euler's approximation, depending on a real parameter \(\mu\), which is well known for its wide applications in numerical computations for vector fields. The authors investigate parametrized difference systems, which can yield normal forms of vector fields and diffeomorphisms together. So the main purpose of this work is to investigate the behavior of normal forms with respect to the \(\mu\)-approximation. Very roughly speaking, the main result is that the normal forms of periodic difference systems and differential systems can be achieved uniformly.
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37C55
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 39A28
zbMATH DE Number: 7489693
zbMATH Keywords: difference system
zbMATH Keywords: differential system
zbMATH Keywords: normal form
zbMATH Keywords: Poincaré domain
reviewed by: Jesus Muciño Raymundo
MaRDI profile type: Publication
full work available at URL: s12346-022-00560-7
OpenAlex ID: W4210281975
cites work: Q4305607
cites work: Q4679023
DOI: 10.1007/S12346-022-00560-7
description: scientific article; zbMATH DE number 7489693