Stability conditions for a fixed point of point maps in the critical case of a pair of complex conjugate roots on the unit circle
type: Item
instance of: scholarly article
title: Stability conditions for a fixed point of point maps in the critical case of a pair of complex conjugate roots on the unit circle
zbMATH Open document ID: 0801.34047
DOI: 10.1007/BF01209381
author: L. Z. Fishman
published in: Mathematical Notes
publication date: 1994-07-21T00:00:00Z
review text: In order to solve the stability problem mentioned in the title, the author obtains formulas for a quantity analogous to the first Lyapunov exponent, expressed in terms of the coefficients of the mappings. These results are used to study the problem of preserving the stability of a compound focus when the system of differential equations is replaced by the corresponding Euler (difference) scheme.
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 578718
zbMATH Keywords: point mappings
zbMATH Keywords: critical case
zbMATH Keywords: Euler difference scheme
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov exponent
MaRDI profile type: Publication
cites work: Computation of the Stability Condition for the Hopf Bifurcation of Diffeomorphisms on $\mathbb{R}^2 $
cites work: Q4341884
cites work: Q3334649
cites work: Q3322411
full work available at URL: https://doi.org/10.1007/bf01209381
OpenAlex ID: W2048647106
description: scientific article; zbMATH DE number 578718