Abstract
For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n - 1) (n - 2) / 2 when n is even, and (n - 1) (n - 2) / 2 when n is odd. Furthermore, these upper bounds are reached. © 2009 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 1401-1409 |
Journal | Journal of Differential Equations |
Volume | 248 |
DOIs | |
Publication status | Published - 15 Mar 2010 |
Keywords
- 16th Hilbert problem
- Algebraic limit cycles
- Limit cycles
- Polynomial vector fields