Results 11 to 20 of about 398,271 (280)
Non-existence of limit cycles via inverse integrating factors
Electronic Journal of Differential Equations, 2011 It is known that if a planar differential systems has an inverse integrating factor, then all the limit cycles contained in the domain of definition of the inverse integrating factor are contained in the zero set of this function.
Leonardo Laura-Guarachi +2 more
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Polynomial inverse integrating factors of quadratic differential systems and other results [PDF]
, 2006 Consultable des del TDXTítol obtingut de la portada digitalitzadaAquesta tesi està dividida en dues parts diferents. En la primera, estudiam els sistemes quadràtics (sistemes polinomials de grau dos) que tenen un invers de factor integrant polinomial. En
Ferragut, Antoni
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Center problem with characteristic directions and inverse integrating factors [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 We consider the center-focus problem for analytic families of planar vector fields having a monodromic singularity with characteristic directions. We give a method to compute the center conditions of the family provided there is an inverse integrating factor whose expression in polar coordinates has the exceptional divisor of the first polar blow-up as
Isaac A. García, Jaume Giné
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The inverse integrating factor and the Poincaré map [PDF]
Transactions of the American Mathematical Society, 2010 This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit.
García, I. A. (Isaac A.) +2 more
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Morphisms and inverse problems for Darboux integrating factors [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2013 Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well understood when the geometry of the underlying curve is non-degenerate. In the general setting, morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight.
Llibre Saló, Jaume +2 more
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Nilpotent centres via inverse integrating factors [PDF]
European Journal of Applied Mathematics, 2016 In this paper, we are interested in the nilpotent centre problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centres. More general objects are considered as the formal inverse integrating factors. However, the existence of a formal inverse integrating factor is not sufficient
Algaba, Antonio +2 more
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Darboux integrability and the inverse integrating factor
Journal of Differential Equations, 2003 Consider planar (real or complex) polynomial vector fields \(X=P(x,y)\partial_x+Q(x,y)\partial_y\) having a Darboux first integral of the form \[ H= f_1^{\lambda_1}\cdots f_p^{\lambda_p} \left( \exp\left( {h_1}\over {g_1} \right) \right)^{\mu_1} \cdots \left( \exp\left({h_q}\over{g_q} \right) \right)^{\mu_q}, \] where \(f_i, g_i\) and \(h_i\) are ...
Chavarriga, Javier +3 more
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Darboux integrating factors: Inverse problems
Journal of Differential Equations, 2011 We discuss planar polynomial vector fields with prescribed Darboux integrating factors, in a nondegenerate affine geometric setting. We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems, and show that the space of vector fields with a given integrating factor, modulo a subspace of ...
Christopher, Colin +3 more
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Formal Inverse Integrating Factor and the Nilpotent Center Problem [PDF]
International Journal of Bifurcation and Chaos, 2016 We are interested in deepening the knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields [Formula: see text]. As formal integrability is not enough to characterize such a center we use a more general object, namely, formal inverse integrating factors [Formula: see ...
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Integrable systems via polynomial inverse integrating factors
Bulletin des Sciences Mathématiques, 2002 The authors study the center problem for planar ordinary differential equations of the form \[ x'=-y+X_s(x,y),\qquad y'=x+Y_s(x,y), \] where \(X_s\) and \(Y_s\) are homogeneous polynomials of degree \(s.\) These systems write in polar coordinates as \(r'=P_s(\varphi)r^s,\) \(\varphi'=1+Q_s(\varphi)r^{s-1}\), where \[ \begin{aligned} P_s(\varphi)&= R_{s+
Chavarriga, J., Giné, J., Grau, M.
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