On Periodic Orbits of Vector Fields in Arbitrary Dimension Via Autonomous and Nonautonomous Inverse Jacobi Multipliers
We investigate periodic orbits of C1 autonomous vector fields in Rn using inverse Jacobi multipliers that may depend explicitly on time. We establish a localization principle for T -periodic orbits in arbitrary dimension, extending known planar results and deriving nonexistence conditions through th...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:dnet:recercat____::9efe7c3a81ac69577693c6b4ada86fef |
| Acceso en línea: | https://doi.org/10.1007/s12346-026-01490-4 https://hdl.handle.net/10459.1/469955 |
| Access Level: | acceso abierto |
| Palabra clave: | Vector fields Inverse Jacobi multipliers Periodic orbits |
| Sumario: | We investigate periodic orbits of C1 autonomous vector fields in Rn using inverse Jacobi multipliers that may depend explicitly on time. We establish a localization principle for T -periodic orbits in arbitrary dimension, extending known planar results and deriving nonexistence conditions through the relation between the time-slices V(0, ·) and V(T , ·). We further characterize hyperbolicity and orbital stability, including a decomposition of characteristic multipliers along invariant surfaces associated with autonomous inverse Jacobi multipliers. A test for the algebraicity of periodic orbits in 3-dimensional vector fields is given based on non-autonomous inverse Jacobi multipliers. The interplay between normalizers, inverse Jacobi multipliers and invariants is analyzed, with applications to the Lorenz and Rössler systems. |
|---|