Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 66, Issue 3, Pages 573-585Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-014-0440-7
Keywords
Non-autonomous systems; inverse Jacobi multipliers; Poincare translation map; periodic solutions
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Funding
- Romanian National Authority for Scientific Research, CNCS-UEFISCDI [PN-II-ID-PCE-2011-3-0094]
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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, translation map I at time T that extends to arbitrary dimensions the fundamental relation for scalar equations, , found in Garcia et al. (Trans Am Math Soc 362:3591-3612, 2010). 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.
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