2011 | OriginalPaper | Buchkapitel
Existence of Invariant Circles for Infinitely Renormalisable Area-Preserving Maps
verfasst von : R. S. MacKay
Erschienen in: Dynamics, Games and Science I
Verlag: Springer Berlin Heidelberg
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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.