The Complexity of Generalized Center Problem

Guangfeng Dong ^[1] ; Changjian Liu ^[2] ; Jiazhong Yang ^[3]
1. [1] Sun Yat-sen University
  
  Sun Yat-sen University
  
  China
2. [2] Soochow University
  
  Soochow University
  
  China
3. [3] Peking University
  
  Peking University
  
  China
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 1, 2015, págs. 11-23
Idioma: inglés
DOI: 10.1007/s12346-015-0131-6
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Resumen
- 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).