On quadratic systems with a degenerate critical point

A. Gasull; R. Prohens

doi:https://doi.org/10.1216/rmjm/1181072107

On quadratic systems with a degenerate critical point

A. Gasull, R. Prohens

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We study phase portraits of quadratic systems with exactly two critical points, one of them degenerate. This problem has already been considered in [10], where part of the results are obtained by computer. Here we deal with these systems in terms of semi-complete families of rotated vector fields. This new approach allows us to prove most of the bifurcation diagrams that we obtain. © 1996 Rocky Mountain Mathematics Consortium.

Original language	English
Pages (from-to)	135-164
Journal	Journal of Differential Geometry
Volume	26
DOIs	https://doi.org/10.1216/rmjm/1181072107
Publication status	Published - 1 Jan 1996

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title = "On quadratic systems with a degenerate critical point",

abstract = "We study phase portraits of quadratic systems with exactly two critical points, one of them degenerate. This problem has already been considered in [10], where part of the results are obtained by computer. Here we deal with these systems in terms of semi-complete families of rotated vector fields. This new approach allows us to prove most of the bifurcation diagrams that we obtain. {\textcopyright} 1996 Rocky Mountain Mathematics Consortium.",

author = "A. Gasull and R. Prohens",

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T1 - On quadratic systems with a degenerate critical point

AU - Gasull, A.

AU - Prohens, R.

PY - 1996/1/1

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N2 - We study phase portraits of quadratic systems with exactly two critical points, one of them degenerate. This problem has already been considered in [10], where part of the results are obtained by computer. Here we deal with these systems in terms of semi-complete families of rotated vector fields. This new approach allows us to prove most of the bifurcation diagrams that we obtain. © 1996 Rocky Mountain Mathematics Consortium.

AB - We study phase portraits of quadratic systems with exactly two critical points, one of them degenerate. This problem has already been considered in [10], where part of the results are obtained by computer. Here we deal with these systems in terms of semi-complete families of rotated vector fields. This new approach allows us to prove most of the bifurcation diagrams that we obtain. © 1996 Rocky Mountain Mathematics Consortium.

U2 - https://doi.org/10.1216/rmjm/1181072107

DO - https://doi.org/10.1216/rmjm/1181072107

M3 - Article

VL - 26

SP - 135

EP - 164

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

ER -