Now showing items 1-8 of 8

    • A method for characterizing nilpotent centers 

      Giné, Jaume; Llibre, Jaume (Elsevier, 2014)
      To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the ...
    • Analytic nilpotent centers as limits of nondegenerate centers revisited 

      García, I. A. (Isaac A.); Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2016-04-25)
      We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré--Liapunov method to detect centers with purely imaginary ...
    • Centers for generalized quintic polynomial differential systems 

      Giné, Jaume; Llibre, Jaume; Valls, Claudia (Rocky Mountain Mathematics Consortium, 2017)
      We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 ...
    • Cyclicity of a class of polynomial nilpotent center singularities 

      García, I. A. (Isaac A.); Shafer, Douglas S. (American Institute of Mathematical Sciences, 2016-04-01)
      In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + ...
    • Cyclicity of Nilpotent Centers with Minimum Andreev Number 

      García, I. A. (Isaac A.) (Springer, 2019-10-07)
      We consider polynomial families of real planar vector fields for which the origin is a monodromic nilpotent singularity having minimum Andree's number. There the centers are characterized by the existence of a formal inverse ...
    • Cyclicity of some symmetric nilpotent centers 

      García, I. A. (Isaac A.) (Elsevier, 2016)
      In this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields. The starting point is identifying a broad family of nilpotent ...
    • Formal inverse integrating factors and the nilpotent center problem 

      García, I. A. (Isaac A.) (World Scientific Publishing, 2016)
      We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to ...
    • The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems 

      Giacomini, Héctor; Giné, Jaume; Llibre, Jaume (Elsevier, 2006)
      In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincaré–Liapunov ...