Results 11 to 20 of about 275,056 (272)

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., Roussarie, R., Rousseau, C.   +2 more
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Parameter Constraints and Real Structures in Quadratic Semicomplete Vector Fields on C3

International Journal of Mathematics and Mathematical Sciences
It 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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Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs

Journal of High Energy Physics, 2023
We present a Sugawara-type construction for boundary charges in 4d BF theory and in a general family of related TQFTs. Starting from the underlying current Lie algebra of boundary symmetries, this gives rise to well-defined quadratic charges forming an ...
Marc Geiller, Florian Girelli, Christophe Goeller, Panagiotis Tsimiklis   +3 more
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Induced Einstein gravity from infinite towers of states

Nuclear Physics B, 2021
We consider four-dimensional quadratic gravity coupled to infinite towers of free massive scalar fields, Weyl fermions and vector bosons. We find that for specific numbers of towers, finite cosmological and Newton constants are induced in the 1-loop ...
A. Kehagias, H. Partouche, B. de Vaulchier   +2 more
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Structurally unstable quadratic vector fields of codimension two: families possessing a finite saddle-node and an infinite saddle-node

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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A new approach to integrals of discretizations by polarization [PDF]

Open Communications in Nonlinear Mathematical Physics
Recently, 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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