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Integrable potentials with cubic and quartic invariants |
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| Affiliation: | Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA |
| Abstract: | The necessary general form for a two-dimensional integrable potential to admit an invariant of the type: I=(xpy-ypx)n+ lower order terms, is obtained and an explicit construction is carried out at n = 3,4. A generalization is made to other similar types of the invariant. |
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