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