3-dimensional piecewise linear and quadratic vector fields with invariant spheres
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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.
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English
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Electronic Journal of Qualitative Theory of Differential Equations, v. 2024, n. 43, 2024.
