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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.
CitationLlibre, J.; Ramírez, R.; Sadovskaia, N. On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves. "Journal of differential equations", 15 Gener 2011, vol. 250, núm. 2, p. 983-999.
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