Displaying similar documents to “Nodal deformations of singularities.”

Differential equations on the plane with given solutions.

R. Ramírez, N. Sadovskaia (1996)

Collectanea Mathematica

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The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.

Quadratic systems with a unique finite rest point.

Bartomeu Coll, Armengol Gasull, Jaume Llibre (1988)

Publicacions Matemàtiques

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We study phase portraits of quadratic systems with a unique finite singularity. We prove that there are 111 different phase portraits without limit cycles and that 13 of them are realizable with exactly one limit cycle. In order to finish completely our study two problems remain open: the realization of one topologically possible phase portrait, and to determine the exact number of limit cycles for a subclass of these systems.

CAPS in Z(2,n)

Kurz, Sascha (2009)

Serdica Journal of Computing

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We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.