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Zbl 1148.37010
Berger, Arno; Son, Doan Thai; Siegmund, Stefan
Nonautonomous finite-time dynamics.
(English)
[J] Discrete Contin. Dyn. Syst., Ser. B 9, No. 3-4, 463-492 (2008). ISSN 1531-3492; ISSN 1553-524X/e

Summary: Nonautonomous differential equations on finite-time intervals play an increasingly important role in applications that incorporate time-varying vector fields, e.g. observed or forecasted velocity fields in meteorology or oceanography which are known only for times $t$ from a compact interval. While classical dynamical systems methods often study the behaviour of solutions as $t\to\pm\infty$, the dynamic partition (originally called the EPH partition) aims at describing and classifying the finite-time behaviour. We discuss fundamental properties of the dynamic partition and show that it locally approximates the nonlinear behaviour. We also provide an algorithm for practical computations with dynamic partitions and apply it to a nonlinear three-dimensional example.
MSC 2000:
*37B55 Nonautonomous dynamical systems
37D05 Hyperbolic orbits and sets
37D10 Invariant manifold theory
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology

Keywords: hyperbolicity; nonautonomous differential equations on finite-time intervals; dynamic partition

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