3-dimensional piecewise linear and quadratic vector fields with invariant spheres
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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Dinamikus rendszer |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.43 |
| Online Access: | http://acta.bibl.u-szeged.hu/88845 |
| Tartalmi kivonat: | 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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| Terjedelem/Fizikai jellemzők: | 27 |
| ISSN: | 1417-3875 |