Approximation of invariant measures

Автор: Osipenko G.S.
Сборник: Iteration Theory, eds. A.N.Sharkovsky, I.M.Sushko
Серия: Grazer Mathematische Berichte
Том: 354
Год издания: 2009
Место издания: Institut fur Mathematik Karl-Franzens-Universitat Graz
Первая страница: 186
Последняя страница: 200
Аннотация: The set of all invariant measures M(f) of a homeomorphism f forms a convex compact in weak topology. The goal is a construction of the set M(f). To obtain an approximation of M(f) we used the notion of the symbolic image with respect to a partition of M. The symbolic image G is a directed graph which is a finite approximation of the mapping f. A flow on the symbol image is a probability distribution on the edges satisfying Kirchhoff low in each vertex: the incoming flow equals outgoing one. The flow is an approximation to some invariant measure. The set of flows on G forms a convex polyhedronM(G) which is an approximation to the set of invariant measures M(f). By considering a sequence of subdivisions one gets the sequence of symbolic images Gk and the approximations M(Gk) which tends to M(f) as diameter of cells goes to zero. An application and numerical examples are given.
Добавил в систему: Осипенко Георгий Сергеевич

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