3-dimensional piecewise linear and quadratic vector fields with invariant spheres

Claudio A. Buzzi; Ana Livia Rodero; Joan Torregrosa

doi:10.14232/ejqtde.2024.1.43

3-dimensional piecewise linear and quadratic vector fields with invariant spheres

Claudio A. Buzzi, Ana Livia Rodero, Joan Torregrosa

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

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Abstract

We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Electronic Journal of Qualitative Theory of Differential Equations
Volume	2024
Issue number	43
DOIs	https://doi.org/10.14232/ejqtde.2024.1.43
Publication status	Published - 2024

Keywords

1-parameter families of closed trajectories
invariant cones
piecewise smooth vector fields with invariant spheres

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10.14232/ejqtde.2024.1.43

https://ddd.uab.cat/record/303170

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title = "3-dimensional piecewise linear and quadratic vector fields with invariant spheres",

abstract = "We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X.",

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year = "2024",

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language = "English",

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T1 - 3-dimensional piecewise linear and quadratic vector fields with invariant spheres

AU - Buzzi, Claudio A.

AU - Rodero, Ana Livia

AU - Torregrosa, Joan

PY - 2024

Y1 - 2024

N2 - We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X.

AB - We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X.

KW - 1-parameter families of closed trajectories

KW - invariant cones

KW - piecewise smooth vector fields with invariant spheres

UR - https://www.scopus.com/pages/publications/85205451891

U2 - 10.14232/ejqtde.2024.1.43

DO - 10.14232/ejqtde.2024.1.43

M3 - Article

SN - 1417-3875

VL - 2024

SP - 1

EP - 27

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

IS - 43

ER -

3-dimensional piecewise linear and quadratic vector fields with invariant spheres

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Keywords

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