Results 11 to 20 of about 274,225 (273)
Twin Vector Fields and Independence of Spectra for Quadratic Vector Fields [PDF]
Journal of Dynamical and Control Systems, 2016 The object of this paper is to address the following question: When is a polynomial vector field on $\mathbb{C}^2$ completely determined (up to affine equivalence) by the spectra of its singularities? We will see that for quadratic vector fields this is not the case: given a generic quadratic vector field there is, up to affine equivalence, exactly one
Valente Ramírez
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Quadratic Hamiltonian Vector Fields
Journal of Differential Equations, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Artes, J.C., Llibre, J.
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Hilbert′s 16th Problem for Quadratic Vector Fields
Journal of Differential Equations, 1994 The second part of Hilbert's 16th problem is to determine the number and relative position of the limit cycles of a polynomial vector field in the plane. This problem remains open even for the case of a vector field whose components are quadratic polynomials.
Dumortier, F. +2 more
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Parameter Constraints and Real Structures in Quadratic Semicomplete Vector Fields on C3
International Journal of Mathematics and Mathematical SciencesIt is a remarkable fact that among the known examples of quadratic semicomplete vector fields on C3, it is always possible to find linear coordinates where the corresponding vector field has all—or “almost all”—coefficients in the real numbers.
Daniel de la Rosa Gómez
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 In 1998, Artés, Kooij and Llibre proved that there exist 44 structurally stable topologically distinct phase portraits modulo limit cycles, and in 2018 Artés, Llibre and Rezende showed the existence of at least 204 (at most 211) structurally unstable ...
Joan Artés, Marcos Mota, Alex Rezende
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Darboux Integrability and Reversible Quadratic Vector Fields
Rocky Mountain Journal of Mathematics, 2005 The authors study the Darboux theory of integrability for reversible polynomial vector fields in \({\mathbb R}^n\). In particular, they define the concept of \(\varphi\)-reversible vector fields for a given involution \(\varphi\) and show that if \(X\) is a \(\varphi\)-reversible quadratic vector field in \({\mathbb R}^2\) such that the set of fixed ...
Llibre, Jaume, Medrado, João Carlos
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Topological and polynomial invariants, moduli spaces, in classification problems of polynomial vector fields [PDF]
, 2014 We describe the origin and evolution of ideas on topological and polynomial invariants and their interaction, in problems of classification of polynomial vector fields.
Schlomiuk, Dana
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A new approach to integrals of discretizations by polarization [PDF]
Open Communications in Nonlinear Mathematical PhysicsRecently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields.
Yuri B. Suris
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Semicompleteness of homogeneous quadratic vector fields [PDF]
Annales de l'Institut Fourier, 2006 We investigate the quadratic homogeneous holomorphic vector fields on C n that are semicomplete, this is, those whose solutions are single-valued in their maximal definition domain. To a generic quadratic vector field we rationally associate some complex numbers that turn out to be integers in the semicomplete case, thus showing that the linear ...
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Stability in quadratic torsion theories
European Physical Journal C: Particles and Fields, 2017 We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors.
Teodor Borislavov Vasilev +3 more
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