Bhatia N.P., Szego G.P. Dynamical Systems: Stability Theory and Applications

Springer-Verlag, 1967. — 416 p. — (Lecture Notes in Mathematics)This book began as a series of lecture notes of the course given by N.P. Bhatia at the Western Reserve University during the Spring of 1965 and the lecture notes of the courses given by G.P. Szego at the "University of Milan during the year 1964-65 and at Case Institute of Technology during the summer of 1965. These courses were meant for different audiences, on one side graduate students in mathematics, and on the other graduate students in systems theory and physics.However in the process of developing these notes we have found a number of other results of interest which we decided to include ( See 1.9, 2.7, 2.8, 2.11, 2.14, 3.3, 3.4, 3.5, 3.7, 3-8, 3-9). Therefore, this monograph is of a dual nature involving both a systematic compilation of known results in dynamical systems and differential equations and a presentation of new Theorems and points of view. As a result, a certain lack of organizational unity and overlapping are evident.
The reader should consider this monograph not as a polished, finished product, but rather as a complete survey of the present state of the art including many new open areas and new problems. Thus, we feel that these notes fit the special aims of this Springer-Verlag series. We do hope that this monograph will be appropriate for a one year graduate course in Dynamical Systems.
This monograph is still devoted to a mixed audience so we have tried to make the presentation of Chapter 1 (Dynamical Systems in Euclidean Space) as simple as possible , using the most simple mathematical techniques and proving in detail all statements, even those which may be obvious to more mature readers. Chapter 2 (Dynamical Systems in Metric Spaces) is more advanced.Chapter 3 has a mixed composition : Sections 3.1, 3.2, 3.6, 3.7 and 3.8 are quite elementary, while the remaining part of the chapter