Stability Theory of Dynamical Systems
From the reviews:
"This is an introductory book intended for beginning graduate students or, perhaps advanced undergraduates. ... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."
Mathematical Reviews, 1972
"The exposition is remarkably clear, definitions are separated explicitly, theorems are often provided together with the motivation for changing one or other hypothesis, as well as the relevance of certain generalisations... This study is an excellent review of the current situation for problems of stability of the solution of differential equations. It is addressed to all interested in non-linear differential problems, as much from the theoretical as from the applications angle."
Bulletin de la Société Mathématique de Belgique, 1975
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A+(x Amer assume asymptotically stable set Chapter characterization closed set compact minimal set compact set component concepts connected set contains continuity axiom continuous function contradiction Corollary D+(M D+(x defines a dynamical Definition dynamical system defined example exists following theorem G. P. SZEGO given Hence homeomorphic implies integer ISBN J+(x Lagrange stable Liapunov functions locally compact locally compact spaces lower-semicontinuous M C Rn Math metric space motion nx N. P. BHATIA Nauk non-empty non-wandering non-wandering points open set ordinary differential equations parallelizable periodic Poisson stable Polon positively invariant real number real-valued function defined recurrent region of attraction rest point semi-trajectory sequence xn set M C X solutions stability properties Stability Theory system X Theorem Theorem 3.9 theory of dynamical tion topological torus trajectory uniform attractor unit circle unstable weak attractor y+(x