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Certain dynamical systems and quasiconformal maps. (English. Russian original) Zbl 0666.30014

Sib. Math. J. 28, No. 4, 674-682 (1987); translation from Sib. Mat. Zh. 28, No. 4(164), 196-206 (1987).
Distortion theorems for solutions to the dynamic systems \(\dot y=u(y)\) are obtained under natural conditions on the behaviour of u in a convex domain \(U\subset R^ n\) with a smooth boundary. The obtained estimates are used for deriving explicit information on the modulus of continuity in the Mori’s distortion theorem for normalized quasiconformal mappings of the plane unit disc.
Reviewer: A.Pierzchalski

MSC:

30C62 Quasiconformal mappings in the complex plane
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
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