The Asymptotic Behavior of Non-extendable Solutions of Quasi-homogeneous Systems
Author(s):
Yuri Vasilievich Churin
Dept. of differential equation
Faculty of Mathematics and Mechanics
Saint-Petersburg State University
Abstract:
This paper explores non-autonomous systems of ordinary differential equations.
Outside of some sphere in phase space the right side of the system is close to
an autonomous homogeneous system which has no bounded solutions and generates
a Morse-Smale dynamical system on the Poincare sphere.
We study the asymptotic behavior of inextensible solutions and
prove that in this case the solution norm increases with no limit,
and its projection onto the unit sphere tends to a non-wandering orbit of the Morse-Smale system.
Keywords
- extendability of solutions
- Morse-Smale systems
- non-autonomous systems
- Poincare sphere
References:
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- Churin Yu. V. [Behavior solutions of quasi-homogeneous system in the neighborhood simple exclusive destinations . ] Nelinejnye dinamicheskie systemy [Nonlinear dynamic systems]. St. Petersburg: Publishing House of St. Petersburg University, 1997, Issue 1, pp. 298-311.
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