Lyapunov exponents and stability
By: N.A. Izobov, Institute of Mathematics, National Academy of Belarus, Minsk, Belarus
Series: Stability oscillations and optimization of systems -- volume 6.; Stability oscillations and optimization of systems -- v.6.
Publisher: CSP/Cambridge Scientific Publishers
Published: 2012
Place of publication: Cambridge, UK
Language: eng
Number of pages: 353
ISBN-13: 9781908106254
Copyright date: 2012
Subjects: Lyapunov exponents; Linear Differential equations
Description: The monograph contains the necessary information from the modern theory of Lyapunov characteristic exponents of ordinary linear differential systems. It is mainly dedicated to the brief description of the results obtained by the author, connected with the development of the following parts: the theory of Perron lower exponents, the freezing method, the theory of exponential and sigma-exponents and their connection with characteristic, central, and general exponents, the dependence of characteristic exponents of linear systems on exponentially decreasing perturbation and the theory of their stability with respect to small perturbations. As an application of those results the author considered the Lyapunov problem on the exponential stability of an ordinary differential system by linear approximation. In the monograph the method of rotations by V.M.Millionschikov is systematically used. This volume is intended for specialists in the asymptotic theory of ordinary differential systems and the stability theory, for post-graduates  and students specialized in the field of differential equations.--
Notes: Includes bibliographical references (pages 327-351) and index.
Table of contents: title: 1. The Lyapunov characteristic exponent and its properties; title: 2. The lower Perron exponent and its properties; title: 3. Central, exponential, and general exponents of a linear system; title: 4. Millionschikov's method of rotations. Attainability of central and exponential exponents and their instability; title: 5. Mutual arrangement of characteristic, exponential central and general exponents of linear systems; title: 6. Lyapunov transformations; title: 7. On the freezing method; title: 8. Linear systems under exponentially decreasing perturbations; title: 9. The higher sigma-exponent of a linear system; title: 10. Stability of characteristic exponents of linear systems; title: 11. Asymptotic stability by linear approximation.