Mathematics and its Applications

3 primary works

Spectral Theory of Families of Self-Adjoint Operators

by Anatolii M. Samoilenko

Published 31 January 1991

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One seIVice topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'j~tre of this series.

Elements of the Mathematical Theory of Multi-Frequency Oscillations

by Anatolii M. Samoilenko

Published 31 October 1991

Translated from the original Russian edition of 1987 (Nauka, Moscow), this volume deals with the theory of multi-frequency oscillations as a motion of a dynamical system which describes a recurrent trajectory on an invariant toroidal manifold of the system. In this way, the invariant toroidal manifo

Multifrequency Oscillations of Nonlinear Systems

by Anatolii M. Samoilenko and R. Petryshyn

Published 7 July 2004

In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.

In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.

This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.