Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Defining Property of Solutions of Nonautonomous Systems C0-close to Morse-Smale Systems

Author(s):

Yuri Vasilievich Churin

Dept. of differential equation
Faculty of Mathematics and Mechanics
Saint-Petersburg State University

Abstract:

The nonautonomous systems of ordinary differential equations defined on smooth manifolds and C0-close to Morse-Smale systems are considered. The theorem giving the defining property of solutions of nonautonomous systems which are C0-close to Morse-Smale systems is formulated.

Keywords

• Morse-Smale systems
• nonautonomous systems
• ordinary differential equations
• smooth manifolds

References:

1. Palis J. On Morse-Smale Dynamical Systems. Topology. 1969. Vol. 8, N. 4. P. 385-404
2. Churin Yu. V. [The asymptotic behavior of non-extendable solutions of quasi-homogeneous systems] Differencial'nie uravnenia i processy upravlenia, 2015. No. 2. P. 14-18. (in Russian) Available at www. math. spbu. ru/diffjournal/RU/numbers/2015. 2/article. 1. 2. html

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