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Flux-minimizing curves for reversible area-preserving maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dewar, Robert L. Meiss, James D. |
| Copyright Year | 1982 |
| Abstract | Abstract Approximately invariant circles for area preserving maps are defined through a mean square flux, (ϕ2-) variational principle. Each trial circle is associated with its image under the area preserving map, and this defines a natural one-dimensional dynamics on the x coordinate. This dynamics is assumed to be semiconjugate to a circle map on an angle variable θ. The consequences of parity ( P -) and time ( T -) reversal symmetries are explored. Stationary points of ϕ2 are associated with orbits. Numerical calculations of ϕ2 indicate a fractal dependence on rotation number, with minima at irrational numbers and maxima at the rationals. For rational frequency there are at least three stationary points of ϕ2: a pair of minimax points, related by PT -reversal, and a stationary, but not minimal, symmetric solution. A perturbation theory without small denominators can be constructed for the symmetric solution. A nonreversible solution for the (0, 1) resonance shows that this solution is highly singular and its circle map is not invertible. |
| Starting Page | 476 |
| Ending Page | 506 |
| Page Count | 31 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/0167-2789(92)90015-F |
| Alternate Webpage(s) | http://amath.colorado.edu/faculty/jdm/papers/FluxMinimizing.pdf |
| Alternate Webpage(s) | http://people.physics.anu.edu.au/~rld105/Dewar_Docs/_preprints/Dewar_Meiss_92.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/0167-2789%2892%2990015-F |
| Volume Number | 57 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
