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

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

We consider the class $\mathcal{X}$ 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 o...

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Bibliographic Details
Main Authors: Claudio Buzzi, Ana Livia Rodero, Joan Torregrosa
Format: Article
Language:English
Published: University of Szeged 2024-08-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
piecewise smooth vector fields with invariant spheres
invariant cones
$1$-parameter families of closed trajectories
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=11057
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