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Existence of invariant circles for infinitely renormalisable area-preserving maps
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MacKay, R. 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 |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of 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.) |
| Date: | 2011 |
| Volume: | Vol.1 |
| Number of Pages: | 809 |
| Page Range: | pp. 631-636 |
| Identification Number: | 10.1007/978-3-642-11456-4_39 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/43709 |
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