ON THE NUMBER OF N-DIMENSIONAL INVARIANT SPHERES IN POLYNOMIAL VECTOR FIELDS OF CN+1

Yudy Bolaños; Jaume Llibre

doi:10.11948/2011011

2011 Volume 1 Issue 2

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Yudy Bolaños, Jaume Llibre. ON THE NUMBER OF N-DIMENSIONAL INVARIANT SPHERES IN POLYNOMIAL VECTOR FIELDS OF CN+1[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 173-182. doi: 10.11948/2011011

Citation:

Yudy Bolaños, Jaume Llibre. ON THE NUMBER OF N-DIMENSIONAL INVARIANT SPHERES IN POLYNOMIAL VECTOR FIELDS OF C^N+1[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 173-182. doi: 10.11948/2011011

ON THE NUMBER OF N-DIMENSIONAL INVARIANT SPHERES IN POLYNOMIAL VECTOR FIELDS OF C^N+1

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

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Abstract

Abstract

We study the polynomial vector fields X=???20110202??? P_i(x₁,..., x_n+1) ∂/∂x_i in Cⁿ⁺¹ with n ≥ 1. Let m_i be the degree of the polynomial P_i. We call (m₁,..., m_n+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.
- polynomial vector fields /
- invariant spheres /
- invariant circles /
- extactic algebraic hypersurface
MSC: 58F14;58F22;34C05

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References

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