Displaying similar documents to “Quadratic systems equivalent by domains to a linear one: global phase portraits.”

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.

Quadratic vector fields with a weak focus of third order.

Joan C. Artés, Jaume Llibre (1997)

Publicacions Matemàtiques

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We study phase portraits of quadratic vector fields with a weak focus of third order at the origin. We show numerically the existence of at least 20 different global phase portraits for such vector fields coming from exactly 16 different local phase portraits available for these vector fields. Among these 20 phase portraits, 17 have no limit cycles and three have at least one limit cycle.

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.

A polynomial with 2k critical values at infinity

Janusz Gwoździewicz, Maciej Sękalski (2004)

Annales Polonici Mathematici

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We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.

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...