Inverse Jacobi multipliers and first integrals for nonautonomous differential systems

Buica, Adriana; García, I. A. (Isaac A.)

doi:https://doi.org/10.1007/s00033-014-0440-7

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Issue date

2015-05-01

Author

Buica, Adriana

García, I. A. (Isaac A.)

Suggested citation

Buica, Adriana; García, I. A. (Isaac A.); . (2015) . Inverse Jacobi multipliers and first integrals for nonautonomous differential systems. Zeitschrift für Angewandte Mathematik und Physik, 2015, vol. 66, p. 573-585. https://doi.org/10.1007/s00033-014-0440-7.

Abstract

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.

URI

http://hdl.handle.net/10459.1/58351

DOI

https://doi.org/10.1007/s00033-014-0440-7

Is part of

Zeitschrift für Angewandte Mathematik und Physik, 2015, vol. 66, p. 573-585