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.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Mar 2010|
- 16th Hilbert problem
- Algebraic limit cycles
- Limit cycles
- Polynomial vector fields