We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N. © 2010 Elsevier Inc.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Jan 2011|
- 16th Hilbert problem
- Algebraic limit cycles
- Limit cycles
- Polynomial vector fields