Home > Articles > Published articles > On the number of n-dimensional invariant spheres in polynomail vector fields of C^n 1 |
Date: | 2011 |
Abstract: | We study in C n+1 the polynomial vector fields X = n +1 ∑ i=1 Pi(x1, . . . , xn+1) ∂/ ∂xi with n ≥ 1 . Let mi be the degree of the polynomial Pi . We call (m1, . . . , mn+1) the degree of X . For these polynomial vector fields X and in function of their degree we provide upper bounds, first for the maximal number of invariant n-dimensional spheres, and second for the maximal number of n- dimensional concentric invariant spheres. |
Grants: | Ministerio de Ciencia y Tecnología MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Polynomial vector fields ; Invariant spheres ; Invariant circles ; Extactic algebraic hypersurface |
Published in: | Journal of Applied Analysis and Computation, Vol. 1 Núm. 2 (2011) , p. 173-182, ISSN 2158-5644 |
Postprint 12 p, 1.9 MB |