Counting uniformly attracting solutions of nonautonomous differential equations. (English) Zbl 1163.34035

Berger, Arno

Discrete Contin. Dyn. Syst., Ser. S 1, No. 1, 15-25 (2008).

The author studies the question how many uniformly attracting solutions a given nonautonomous differential equations has. As examples in the paper show, there can be infinitely many such solutions, even if the right hand side is real-analytic and one only counts solutions in a certain compact subset of the phase space. Only finitely many uniformly attracting solutions, however, exist in the case when the right hand side is period, asymptotically autonomous or a polynomial with bounded time-dependent coefficients.

Reviewer: Martin Rasmussen (London)

MSC:

34D45	Attractors of solutions to ordinary differential equations
37C70	Attractors and repellers of smooth dynamical systems and their topological structure
34C07	Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
37C60	Nonautonomous smooth dynamical systems

Keywords:

nonautonomous dynamical system; attractor; repellor; polynomial differential equation; Poincaré map