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Boundaries of attractors as omega limit sets
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UNSPECIFIED (2005) Boundaries of attractors as omega limit sets. STOCHASTICS AND DYNAMICS, 5 (1). pp. 97-109. ISSN 0219-4937.
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Abstract
When a system of ordinary differential equations on R-d have an attractor A given as the omega-limit set of a compact set D [A = Omega(D) ], then provided that D contains A necessarily partial derivative A = Omega(partial derivative D), i.e. the boundary of the attractor is the omega limit set of the boundary of D. In general only a weaker result, partial derivative A subset of Omega(partial derivative D), can be shown to hold for random attractors arising from systems of stochastic ordinary differential equations, where now D is any compact set such that A is contained in D with a positive probability. However, if in addition A boolean AND D is empty with positive probability, then in fact A = Omega(partial derivative D).
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | STOCHASTICS AND DYNAMICS | ||||
Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | ||||
ISSN: | 0219-4937 | ||||
Official Date: | March 2005 | ||||
Dates: |
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Volume: | 5 | ||||
Number: | 1 | ||||
Number of Pages: | 13 | ||||
Page Range: | pp. 97-109 | ||||
Publication Status: | Published |
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