Inverse Jacobi multipliers and first integrals for nonautonomous differential systems
In this paper we consider nonautonomous differential systems of arbitrary dimension and first find expressions for their inverse Jacobi multipliers and first integrals in some nonautonomous invariant set in terms of the solutions of the differential system. Given an inverse Jacobi multiplier $V$, we...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/58351 |
| Online Access: | https://doi.org/10.1007/s00033-014-0440-7 http://hdl.handle.net/10459.1/58351 |
| Access Level: | Open access |
| Keyword: | Non-autonomous systems Inverse Jacobi multipliers |
| Summary: | In this paper we consider nonautonomous differential systems of arbitrary dimension and first find expressions for their inverse Jacobi multipliers and first integrals in some nonautonomous invariant set in terms of the solutions of the differential system. Given an inverse Jacobi multiplier $V$, we find a relation between the Poincar\'{e} translation map $\Pi$ at time $T$ that extends to arbitrary dimensions the fundamental relation for scalar equations, $V(T,\Pi(x))=V(0,x)\Pi'(x)$, found in Trans. Amer. Math. Soc. 362 (2010), 3591-3612. The main result guarantees the existence of continua of $T$-periodic solutions for $T$-periodic systems in the presence of $T$-periodic first integrals and inverse Jacobi multipliers. |
|---|