Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Bhatia, G. Szegö (1970)
Stability theory of dynamical systems
Differential Equations, Vol. 40, No. 8, 2004, pp. 1096–1105. Translated from Differentsial'nye Uravneniya, Vol. 40, No. 8, 2004, pp. 1033–1042. Original Russian Text Copyright c 2004 by Kalitin. ORDINARY DIFFERENTIAL EQUATIONS Lyapunov Stability and Orbital Stability of Dynamical Systems B. S. Kalitin Belarus State University, Minsk, Belarus Received April 17, 2002 1. INTRODUCTION In the development of Lyapunov stability theory [1], investigation methods were improved in two areas of study, stability of equilibria and stability of motions. From the mathematical viewpoint, the former is a special case of the latter. The di erence between them was emphasized later, when arbitrary invariant sets of abstract dynamical systems, rather then equilibrium points, became an object of intensive studies. Let us introduce necessary notation and de nitions [2]. Let R be the real line, and let X be an arbitrary nonempty set, which, together with a distance function d : X X ! R ,is a metric space. A dynamical system on X is a triple (X; R;), where :(x;t) ! xt is a phase mapping of X R into X . For each element x of X , the mapping x : t ! xt is called the
Differential Equations – Springer Journals
Published: Jan 6, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.