Displaying similar documents to “Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.”

New sufficient conditions for a center and global phase portraits for polynomial systems.

Hector Giacomini, Malick Ndiaye (1996)

Publicacions Matemàtiques

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In this paper we consider cubic polynomial systems of the form: x' = y + P(x, y), y' = −x + Q(x, y), where P and Q are polynomials of degree 3 without linear part. If M(x, y) is an integrating factor of the system, we propose its reciprocal V (x, y) = 1 / M(x,y) as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the...

Basic algebro-geometric conceps in the study of planar polynomial vector fields.

Dana Schlomiuk (1997)

Publicacions Matemàtiques

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In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.

Five limit cycles for a simple cubic system.

Noel G. Lloyd, Jane M. Pearson (1997)

Publicacions Matemàtiques

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We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.

The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations

Waldo Arriagada-Silva, Christiane Rousseau (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we study equivalence classes of generic 1 -parameter germs of real analytic families 𝒬 ε unfolding codimension 1 germs of diffeomorphisms 𝒬 0 : ( ℝ , 0 ) → ( ℝ , 0 ) with a fixed point at the origin and multiplier - 1 , under (weak) analytic conjugacy. These germs are generic unfoldings of the flip bifurcation. Two such germs are analytically conjugate if and only if their second iterates, 𝒫 ε = 𝒬 ε ∘ 2 , are analytically conjugate. We give a complete modulus of analytic classification: this modulus is an unfolding...