Simultaneous Bifurcation of Limit Cycles and Critical Periods [PDF]
, 2022 Altres ajuts: Acord transformatiu CRUE-CSICThe present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane.
Oliveira, Regilene +2 more
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From an iteration formula to Poincaré’s Isochronous Center Theorem for holomorphic vector fields [PDF]
Proceedings of the American Mathematical Society, 2007 We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H. Poincaré, for the condition under which a singularity of a holomorphic vector field is an isochronous center.
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The criticality of reversible quadratic centers at the outer boundary of its period annulus [PDF]
, 2022 This paper deals with the period function of the reversible quadratic centers where . Compactifying the vector field to , the boundary of the period annulus has two connected components, the center itself and a polycycle. We call them the inner and outer
Marín Pérez, David +2 more
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Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group [PDF]
, 2005 Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in ...
Allan R. Wilks +5 more
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On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces [PDF]
, 2014 We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with $2\pi$-periodic coefficients, for initial data living in a space of quasiperiodic functions.
Lastra, Alberto, Malek, Stéphane
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Center problem for systems with two monomial nonlinearities [PDF]
, 2016 We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family.
Gasull i Embid, Armengol +2 more
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Topological classification of polynomial complex differential equations with all the critical points of centre type [PDF]
, 2010 In this paper we study the global phase portrait of complex polynomial differential equations of degree n of the form z˙ = f(z), having all their critical points of center type.
Gasull i Embid, Armengol +2 more
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, 2006 We study the complexification of the one-dimensional Newtonian particle in a monomial potential. We discuss two classes of motions on the associated Riemann surface: the rectilinear and the cyclic motions, corresponding to two different classes of real ...
Abenda +40 more
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On the analytic commutator for Λ–Ω differential systems [PDF]
, 2023 In this paper, we give the necessary and sufficient conditions for some Λ–Ω differential systems to have an analytic commutator, use these properties to judge the origin point of the Λ–Ω differential systems to be an isochronous ...
Zhou Zhengxin
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Bifurcation of critical periods from Pleshkan's isochrones [PDF]
, 2010 Pleshkan proved in 1969 that, up to a linear transformation and a constant rescaling of time, there are four isochrones in the family of cubic centers with homogeneous nonlinearities ℓ3.
Grau, Maite, Villadelprat Yagüe, Jordi
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