Resumen de The Complexity of Generalized Center Problem

Guangfeng Dong, Changjian Liu, Jiazhong Yang

• In this paper, we study the complexity of generalized center problem by looking for the lower bounds of the maximal possible saddle order M(p, q, n) of planar polynomial differential equations of arbitrary degree n admitting any p : −q saddle type resonance between the eigenvalues. We prove that, for any given positive integers p and q, and sufficiently big integer n, M(p, q, n) can grow at least as rapidly as 2n2. This result significantly improves all the known lower bounds which are at most n2 + O(n).