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Displaying similar documents to “Quadratic vector fields with a weak focus of third order.”

Chordal cubic systems.

Marc Carbonell, Jaume Llibre (1989)

Publicacions Matemàtiques

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We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincaré sphere are isolated and have linear part non-identically zero.

Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system.

Li Jibin, Liu Zhenrong (1991)

Publicacions Matemàtiques

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In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points. Using detection functions, we present explicit formulas for the global and local bifurcations of the flow. We exhibit various patterns of compound eyes of limit cycles. These results are concerned with the posed by V. I. Arnold in 1977.

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

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Let H d be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if f ∈ H d and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of H d containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate...

A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

Peter Smith (1990)

Revista Matemática de la Universidad Complutense de Madrid

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Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application...

Nontrivial critical points of asymptotically quadratic functions at resonances

Michal Fečkan (1997)

Annales Polonici Mathematici

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Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.

Existence of solutions for some elliptic problems with critical Sobolev exponents.

Mario Zuluaga (1989)

Revista Matemática Iberoamericana

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Let Ω be a bounded domain in Rn with n ≥ 3. In this paper we are concerned with the problem of finding u ∈ H0 1 (Ω) satisfying the nonlinear elliptic problems Δu + |u|(n+2/n-2) + f(x) = 0  in Ω and u(x) = 0 on ∂Ω, and Δu + u + |u|(n+2/n-2) + f(x) = 0  in Ω and u(x) = 0 on ∂Ω, when of f ∈ L∞(Ω). ...