Search Results - "Llibre, Jaume"

Periods of Self-Maps on S2 Via their Homology by Llibre, Jaume

“…As usual, we denote a 2-dimensional sphere by S 2 . We study the periods of periodic orbits of the maps f : S 2 → S 2 that are either continuous or C 1 with…”
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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities by Llibre, Jaume

“…Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the…”
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Integrability and Limit Cycles via First Integrals by Llibre, Jaume

“…In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a…”
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On the 16th Hilbert Problem for Discontinuous Piecewise Polynomial Hamiltonian Systems by Li, Tao, Llibre, Jaume

“…In this paper we study the maximum number of limit cycles of the discontinuous piecewise differential systems with two zones separated by the straight line y =…”
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The Classical and Improved Euler-Jacobi Formula and Polynomial Vector Fields in Rn by Llibre, Jaume, Valls, Claudia

“…The classical and the new Euler-Jacobi formulae for simple and double points provide an algebraic relation between the singular points of a polynomial vector…”
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Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II) by He, Dongping, Llibre, Jaume

“…In our previous work, we have studied the limit cycles for a class of discontinuous piecewise quadratic polynomial differential systems with a non-regular line…”
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Global centers of a family of cubic systems by Appis, Raul Felipe, Llibre, Jaume

“…Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ′ = y , y ′ = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x…”
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Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials by Gao, Fabao, Llibre, Jaume

“…The global dynamics of a cosmological model based on Hořava–Lifshitz gravity in the presence of curvature is described by using the qualitative theory of…”
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Correction to: Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II) by He, Dongping, Llibre, Jaume

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Global Dynamics of a System Coming from the Study of a Static Star by Llibre, Jaume, Valls, Claudia

“…We classify the global dynamics of a one-parameter family of planar quadratic polynomial differential systems which for some interval of values of its…”
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Phase Portraits of Uniform Isochronous Centers with Homogeneous Nonlinearities by Llibre, Jaume, Valls, Claudia

“…We classify the phase portraits in the Poincaré disc of the differential equations of the form x ′ = − y + x f ( x , y ) , y ̇ = x + y f ( x , y ) where f ( x…”
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On the Integrability of a Four-Prototype Rössler System by Llibre, Jaume, Valls, Claudia

“…We consider a four-prototype Rossler system introduced by Otto Rössler among others as prototypes of the simplest autonomous differential equations (in the…”
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On the Poincaré–Bendixson Formula for Planar Piecewise Smooth Vector Fields by Li, Shimin, Liu, Changjian, Llibre, Jaume

“…The topological index, or simply the index, of an equilibrium point of a vector field is an integer which saves important information about the local phase…”
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The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y=xn by Llibre, Jaume, Valls, Claudia

“…We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic…”
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The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 6 by Dong, Guangfeng, Llibre, Jaume

“…In this paper we study the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear parts are…”
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Darboux theory of integrability in Tn by Llibre, Jaume, Valls, Claudia

“…We develop the Darboux theory of integrability for polynomial vector fields in the n -dimensional torus T n . We also provide the maximum number of invariant…”
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The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems by Benterki, Rebiha, Llibre, Jaume

“…We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a…”
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Twin Polynomial Vector Fields of Arbitrary Degree by Llibre, Jaume, Valls, Claudia

“…In this paper we study polynomial vector fields on C 2 of degree larger than 2 with n 2 isolated singularities. More precisely, we show that if two polynomial…”
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A note on the Dziobek central configurations by LLIBRE, JAUME

“…For the Newtonian n-body problem in ℝn–2 with n ≥ 3 we prove that the following two statements are equivalent. (a) Let x be a Dziobek central configuration…”
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Existence of Periodic Solutions for a Class of Second Order Ordinary Differential Equations by Garcia, Antonio, Llibre, Jaume

“…We provide sufficient conditions for the existence of a periodic solution for a class of second order differential equations of the form x ¨ + g ( x ) = ε f (…”
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