Rotationally-ordered periodic orbits for multiharmonic area-preserving twist maps

J. A. Ketoja, R. S. MacKay

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


The Poincaré-Birkhoff theorem guarantees existence of at least two rotationally-ordered periodic orbits of each rational rotation number for each area-preserving twist map. For many maps, however, there are more than two. We prove this for maps near a non-degenerate multi-well anti-integrable limit, and deduce an intricate bifurcation diagram for rotationally-ordered periodic orbits in so-called "multiharmonic" families. Our results are motivated and supported by numerical investigations of the reversible 2-harmonic family. We believe the results will be helpful for understanding the breakup boundary for invariant circles in multiharmonic families, which numerically exhibits a Cantor set of cusps.

Original languageEnglish
Pages (from-to)388-398
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Issue number4
Publication statusPublished - 15 Jun 1994
MoE publication typeNot Eligible


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