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ROTATIONALLY-ORDERED PERIODIC-ORBITS FOR MULTIHARMONIC AREA-PRESERVING TWIST MAPS
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UNSPECIFIED (1994) ROTATIONALLY-ORDERED PERIODIC-ORBITS FOR MULTIHARMONIC AREA-PRESERVING TWIST MAPS. PHYSICA D, 73 (4). pp. 388-398. ISSN 0167-2789.
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Abstract
The Poincare-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.
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: | PHYSICA D | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 15 June 1994 | ||||
Dates: |
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Volume: | 73 | ||||
Number: | 4 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 388-398 | ||||
Publication Status: | Published |
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