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[1894] Artykuł: Symmetry Breaking and Fractal Dependence on Initial Conditions in Dynamical Systems: Ordinary Differential Equations of Thermal ConvectionCzasopismo: Chaos Solitons & Fractals Tom: 9, Zeszyt: 10, Strony: 1723-1732ISSN: 0960-0779 Wydawca: PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND Opublikowano: Pażdziernik 1998 Autorzy / Redaktorzy / Twórcy
Grupa MNiSW: Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A) Punkty MNiSW: 0 Klasyfikacja Web of Science: Article Pełny tekst DOI Web of Science YADDA/CEON |
A system of n = 3 ordinary differential equations with discrete symmetry describing thermal convection in fluids is investigated. It is shown that the boundary structure of basins of co-existing, non-symmetric attractors, which are present after symmetry breaking, is determined by stable manifolds of the symmetric repellers. Moreover, boundary components fall into two classes: separating boundaries, dim(W S ) = n - 1, or non-separating boundaries, dim(W S ) < n - 1, where n is the dimension of the phase space. Geometry of a basin boundary, formed in the regular regime of dynamics is explained and shown to be quasi-fractal.