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: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2026 |
| País: | España |
| Recursos: | Universitat de Lleida (UdL) |
| Repositório: | Repositori Obert UdL |
| OAI Identifier: | oai:dnet:.___________::54dcfb4e5517823266db7e0b790beb4e |
| Acesso em linha: | https://doi.org/10.1007/s12346-026-01490-4 https://hdl.handle.net/10459.1/469955 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Vector fields Inverse Jacobi multipliers Periodic orbits |
| Resumo: | 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. |
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