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SYMMETRY DETECTIVES FOR SBR ATTRACTORS
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UNSPECIFIED (1995) SYMMETRY DETECTIVES FOR SBR ATTRACTORS. NONLINEARITY, 8 (6). pp. 1027-1037. ISSN 0951-7715.
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Abstract
Let Gamma be a finite group acting on R(n) and let x(0) be an initial point for a Gamma-equivariant map f : R(n) --> R(n). The question of determining the symmetries of the omega-limit set omega f(x(0)) is discussed by Barany et al and Dellnitz et al. The methods introduced therein are based on the notion of a symmetry detective. Detectives replace the question of determining the symmetries of the set of omega f(x(0)) by the easier question of determining the symmetries of a point in an associated space W. The detective theorem of Barany et al has a limitation in that its implementation tacitly assumes that omega f(x(0)) contains a point of trivial isotropy; this assumption is explicit in Dellnitz et al. In this paper we extend the ideas of these authors to present sufficient conditions for an equivariant polynomial phi :R(n) --> W to be a detective, even when the omega-limit set is contained in a proper fixed-point subspace. We show that W need only satisfy the conditions given by Barany et al and Dellnitz et al while the map phi has to satisfy certain conditions in addition to the ones listed by these authors. We also present a density theorem for such detectives and we show that the detective for rings of p coupled cells (nearest-neighbour coupling) with D-p symmetry first given by Barany et al is a detective for all (SBR) attractors.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | November 1995 | ||||
Dates: |
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Volume: | 8 | ||||
Number: | 6 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 1027-1037 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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