ROTATIONALLY-ORDERED PERIODIC-ORBITS FOR MULTIHARMONIC AREA-PRESERVING TWIST MAPS
UNSPECIFIED. (1994) ROTATIONALLY-ORDERED PERIODIC-ORBITS FOR MULTIHARMONIC AREA-PRESERVING TWIST MAPS. PHYSICA D, 73 (4). pp. 388-398. ISSN 0167-2789Full text not available from this repository.
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|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Journal or Publication Title:||PHYSICA D|
|Publisher:||ELSEVIER SCIENCE BV|
|Date:||15 June 1994|
|Number of Pages:||11|
|Page Range:||pp. 388-398|
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