Abstract
We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. © 2003 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 374-380 |
Journal | Journal of Differential Equations |
Volume | 198 |
DOIs | |
Publication status | Published - 10 Apr 2004 |
Keywords
- Limit cycles
- Quadratic vector fields