On the Poincaré Problem
We derive some restrictions on the possible degrees of algebraic invariant curves and on the possible form of algebraic integrating factors, for plane polynomial vector fields whose stationary points at infinity satisfy a certain genericity condition. The method is elementary, and we show by example...
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| Published in | Journal of Differential Equations Vol. 166; no. 1; pp. 51 - 78 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.09.2000
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| Online Access | Get full text |
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| Summary: | We derive some restrictions on the possible degrees of algebraic invariant curves and on the possible form of algebraic integrating factors, for plane polynomial vector fields whose stationary points at infinity satisfy a certain genericity condition. The method is elementary, and we show by example that it also yields strong results for certain non-generic vector fields. |
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| ISSN: | 0022-0396 1090-2732 |
| DOI: | 10.1006/jdeq.2000.3801 |