Displaying similar documents to “Bifurcations of limit cycles from cubic Hamiltonian systems with a center and a homoclinic saddle-loop.”

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

Mihajlova, Ana (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08. We obtain an upper bound for the number of zeros of the Abelian integral. The work was partially supported by contract No 15/09.05.2002 with the Shoumen University “K. Preslavski”, Shoumen, Bulgaria.

Simple examples of one-parameter planar bifurcations.

Armengol Gasull, Rafel Prohens (2000)

Extracta Mathematicae

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In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.

Inverse problems in the theory of analytic planar vector fields.

Natalia Sadovskaia, Rafael O. Ramírez (1998)

Revista Matemática Iberoamericana

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In this communication we state and analyze the new inverse problems in the theory of differential equations related to the construction of an analytic planar verctor field from a given, finite number of solutions, trajectories or partial integrals. Likewise, we study the problem of determining a stationary complex analytic vector field Γ from a given, finite subset of terms in the formal power series (...).

The null divergence factor.

Javier Chavarriga, Héctor Giacomini, Jaume Giné (1997)

Publicacions Matemàtiques

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Let (P,Q) be a C vector field defined in a open subset U ⊂ R. We call a null divergence factor a C solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) V. In previous works it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux...

Hopf-like bifurcations in planar piecewise linear systems.

Emilio Freire, Enrique Ponce, Francisco Torres (1997)

Publicacions Matemàtiques

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Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving rise to limit cycles are pointed out.