Previous |  Up |  Next

Article

Keywords:
invariant submanifold; variational equation; moving orthogonal system
Summary:
The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in $\mathbb{R}^3$. An application concerning computation of a derivative of a scalar Poincaré mapping is given.
References:
[1] L. Adamec: A note on a generalization of Diliberto’s theorem for certain differential equations of higher dimension. (to appear). MR 2125152 | Zbl 1099.37032
[2] I. Agricola, T. Friedrich: Global Analysis. American Mathematical Society, Rode Island, 2002. MR 1998826
[3] C. Chicone: Bifurcation of nonlinear oscillations and frequency entrainment near resonance. SIAM J. Math. Anal. 23 (1992), 1577–1608. DOI 10.1137/0523087 | MR 1185642
[4] C. Chicone: Lyapunov-Schmidt reduction and Melnikov integrals for bifurcation of periodic solutions in coupled oscillators. J. Differ. Equations 112 (1994), 407–447. DOI 10.1006/jdeq.1994.1110 | MR 1293477
[5] C. Chicone: Ordinary Differential Equations with Applications. Springer, New York, 1999. MR 1707333 | Zbl 0937.34001
[6] Ph. Hartman: Ordinary Differential Equations. John Wiley, New York, 1964. MR 0171038 | Zbl 0125.32102
[7] M. Y. Li, J. S. Muldowney: Dynamics of differential equations on invariant manifolds. J. Differ. Equations 168 (2000), 295–320. DOI 10.1006/jdeq.2000.3888 | MR 1808452
Partner of
EuDML logo