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Existence of invariant circles for infinitely renormalisable area-preserving maps
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MacKay, Robert S. (2011) Existence of invariant circles for infinitely renormalisable area-preserving maps. In: Peixoto, Mauricio Matos and Pinto, Alberto Adrego and Rand, D. A. (David A.), (eds.) Dynamics, Games and Science I. Springer proceedings in mathematics, Vol.1 . Berlin ; Heidelberg ; New York: Springer, pp. 631-636. ISBN 9783642114564
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Official URL: http://dx.doi.org/10.1007/978-3-642-11456-4_39
Abstract
Existence of an invariant circle for any orientation-preserving 2D map whose orbit under renormalisation remains forever in a certain bounded subset is proved. The construction dates back to 1984. It was stimulated by a preprint by David Rand doing the same for the dissipative case. To include the general case, notably area-preserving, required a variation on his idea.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Springer proceedings in mathematics | ||||
Publisher: | Springer | ||||
Place of Publication: | Berlin ; Heidelberg ; New York | ||||
ISBN: | 9783642114564 | ||||
ISSN: | 2190-5614 | ||||
Book Title: | Dynamics, Games and Science I | ||||
Editor: | Peixoto, Mauricio Matos and Pinto, Alberto Adrego and Rand, D. A. (David A.) | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.1 | ||||
Number of Pages: | 809 | ||||
Page Range: | pp. 631-636 | ||||
DOI: | 10.1007/978-3-642-11456-4_39 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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