An inverse approach to the center problem [PDF]
, 2019 We consider analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y)) and Y= Y(x, y)) start at least with terms of second order.
Llibre, Jaume +2 more
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Some open problems in low dimensional dynamical systems [PDF]
, 2020 The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve some of the ...
Gasull, Armengol
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Periods of solutions of periodic differential equations [PDF]
, 2016 Smooth non-autonomous T-periodic differential equations x'(t)=f(t,x(t)) defined in \R\K^n, where \K is \R or \C and n 2 can have periodic solutions with any arbitrary period~S. We show that this is not the case when n=1.
Cimà, Anna +2 more
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Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems
, 2012 We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the perturbation.
Andronov +10 more
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Flat systems, equivalence and trajectory generation [PDF]
, 2003 Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework.
Martin, Phillipe +2 more
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Lie algebras and geometric complexity of an isochronous center condition [PDF]
, 2018 International audienceUsing the mould formalism introduced by Jean Ecalle, we define and study the geometric complexity of an isochronous center condition. The role played by several Lie ideals is discussed coming from the interplay between the universal
Cresson, Jacky, Palafox, Jordy
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On the separatrix graph of a rational vector field on the Riemann sphere
, 2020 We consider the rational flow $\xi_R(z)= R(z) (d/dz)$ where $R$ is given by the quotient of two polynomials without common factors on the Riemann sphere. The separatrix graph $\Gamma_R$ is the boundary between trajectories with different properties.
Dias, Kealey, Garijo, Antonio
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Centre and isochronicity conditions for systems with homogeneous nonlinearities [PDF]
, 1995 We study the centre-focus problem for systems with homogeneous nonlinearities. In the centre case we study the characterization of the isochronous centres. More explicitly, we derive six necessary conditions to be a centre and six necessary conditions
Gasull Embid, Armengol +2 more
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Qualitative theory of differential equations in the plane and in the space, with emphasis on the center-focus problem and on the Lotka-Volterra systems [PDF]
, 2020 Departament responsable de la tesi: Departament de Matemàtiques.Vegeu resum vrs1de1.pdf.Vegeu resum vrs1de1 ...
Ramírez Sadovski, Valentí +1 more
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Some Questions around The Hilbert 16th Problem
, 2005 We present some questions and suggestion on the second part of the Hilbert 16th ...
Taghavi, Ali
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