Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An improved estimate for the highest Lyapunov exponent in the method of freezing
HTML articles powered by AMS MathViewer

by G. I. Eleutheriadis
Proc. Amer. Math. Soc. 125 (1997), 2931-2937
DOI: https://doi.org/10.1090/S0002-9939-97-03952-X

Abstract:

Let $\dot x=A(t)x$ and $\lambda _k(t)$ be the eigenvalues of the matrix $A(t)$. The main result of the Method of Freezing states that if $\sup _J \|A(t)\|\leq M$, $\sup _J\max _{1\leq k\leq n}\mathrm {Re} \lambda _k(t)\leq \rho$ and $\sup _J(\|A(t)-A(s)\|/|t-s|)\leq \delta$, then \[ x_{\max }\leq \rho +2M\lambda _\delta ,\] for the highest exponent $x_{\max }$ of the system, where \[ \lambda _\delta =\left (\frac {C_n\delta }{4M^2}\right )^{\frac {1}{n+1}}.\] The previous best known value $C_n=\frac {n(n+1)}{2}$ and the substantially smaller values of $C_n$ are reduced to the still smaller value.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34D08
  • Retrieve articles in all journals with MSC (1991): 34D08
Bibliographic Information
  • G. I. Eleutheriadis
  • Affiliation: Ektenepol, 14/3, 67100, Xanthi, Greece
  • Received by editor(s): May 1, 1996
  • Communicated by: Hal L. Smith
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2931-2937
  • MSC (1991): Primary 34D08
  • DOI: https://doi.org/10.1090/S0002-9939-97-03952-X
  • MathSciNet review: 1403124