Translator Disclaimer
1995 Quadratic Lyapunov functions for linear skew-product flows and weighted composition operators
C. Chicone, Yu. Latushkin
Differential Integral Equations 8(2): 289-307 (1995).

Abstract

The Daleckij-Krein method for constructing a quadratic Lyapunov function for the equation $f'=Df(t)$ in Hilbert space is extended to include the case of an unbounded operator $D$ that generates a $C_0$-group. The extension is applied to obtain a quadratic Lyapunov function for the case of a group of weighted composition operators generated by a flow on a compact metric space together with a cocycle over this flow. These results are used to characterize the hyperbolicity of linear skew-product flows in terms of the existence of such a Lyapunov function. Also, the "trajectorial" method for constructing the Lyapunov function is discussed. Interrelations with Schrödinger, Riccati and Hamiltonian equations are discussed and an application to geodesic flows on two-dimensional Riemannian manifolds is given.

Citation

Download Citation

C. Chicone. Yu. Latushkin. "Quadratic Lyapunov functions for linear skew-product flows and weighted composition operators." Differential Integral Equations 8 (2) 289 - 307, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0813.34056
MathSciNet: MR1296125

Subjects:
Primary: 47D06
Secondary: 34C35, 34G10, 47B38, 58F17

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.8 • No. 2 • 1995
Back to Top