Displaying similar documents to “Existence and distribution of limit cycles in a Hamiltonian system.”

Uniqueness of limit cycles bounded by two invariant parabolas

Eduardo Sáez, Iván Szántó (2012)

Applications of Mathematics

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In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.

Matchings Extend to Hamiltonian Cycles in 5-Cube

Fan Wang, Weisheng Zhao (2018)

Discussiones Mathematicae Graph Theory

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Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.

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...

On theH-Force Number of Hamiltonian Graphs and Cycle Extendability

Erhard Hexel (2017)

Discussiones Mathematicae Graph Theory

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The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given. Such graphs, for which h(G) assumes the lower bound are characterized by a cycle extendability property. The H-force number of hamiltonian graphs which are exactly 2-connected can be calculated by a decomposition formula.

Pancyclism and small cycles in graphs

Ralph Faudree, Odile Favaron, Evelyne Flandrin, Hao Li (1996)

Discussiones Mathematicae Graph Theory

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We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u)+d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u)+d(v) ≥ n+z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m for each 3 ≤ m ≤ max (dC(u,v)+1, [(n+19)/13]), d C ( u , v ) being the distance of u and v on a hamiltonian cycle...