On variational systems along the trajectories of a stable compact invariant set of an autonomous complex-analytic system of differential equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 0988.34038
author: I. L. Zinchenko
publication date: 2001-10-03T00:00:00Z
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1577606
zbMATH Keywords: variational systems
zbMATH Keywords: stable compact invariant set
zbMATH Keywords: complex-analytic differential equation
MaRDI profile type: Publication
title: On variational systems along the trajectories of a stable compact invariant set of an autonomous complex-analytic system of differential equations
published in: Differential Equations
review text: Let \(E \in \mathbb{C}^n\) be a stable compact invariant set of the autonomous complex-analytic system \(\dot{w}=f(w)\). The author shows that there exists a dense set \(E^* \subset E\) such that every variational equation along an orbit through a point \(w^* \in E\) is proper, i.e. the sum of the Lyapunov exponents equals the average NEWLINE\[NEWLINE\lim_{t\to\infty} 1/t \int_0^t \text{Re} [\text{Sp} \frac{\partial f}{\partial w}(w(t,w^*))]dt.NEWLINE\]NEWLINE The author also gives a condition for \(E^* = E\).
reviewed by: S. Siegmund
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description: scientific article