Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in R^3
We consider the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional algebraic torus T2(l, m, n) = {(x, y, z) ∈ R3: (x2l + y2m - r2)2 + z2n - 1 = 0}, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150652 |
| Acceso en línea: | https://ddd.uab.cat/record/150652 https://dx.doi.org/urn:doi:10.1007/s10884-013-9315-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial vector fields Invariant parallel Invariant meridian Limit cycles Periodic orbits 2-dimensional torus |
| Sumario: | We consider the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional algebraic torus T2(l, m, n) = {(x, y, z) ∈ R3: (x2l + y2m - r2)2 + z2n - 1 = 0}, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore we analyze when these invariant meridians or parallels are limit cycles. |
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