| Title:
|
A note on the fundamental matrix of variational equations in $\mathbb{R}^3$ (English) |
| Author:
|
Adamec, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
411-418 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
invariant submanifold |
| Keyword:
|
variational equation |
| Keyword:
|
moving orthogonal system |
| MSC:
|
34C30 |
| MSC:
|
34D10 |
| MSC:
|
37C10 |
| MSC:
|
37E99 |
| idZBL:
|
Zbl 1052.37014 |
| idMR:
|
MR2032478 |
| DOI:
|
10.21136/MB.2003.133999 |
| . |
| Date available:
|
2009-09-24T22:11:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133999 |
| . |
| Reference:
|
[1] L. Adamec: A note on a generalization of Diliberto’s theorem for certain differential equations of higher dimension.(to appear). Zbl 1099.37032, MR 2125152 |
| Reference:
|
[2] I. Agricola, T. Friedrich: Global Analysis.American Mathematical Society, Rode Island, 2002. MR 1998826 |
| Reference:
|
[3] C. Chicone: Bifurcation of nonlinear oscillations and frequency entrainment near resonance.SIAM J. Math. Anal. 23 (1992), 1577–1608. MR 1185642, 10.1137/0523087 |
| Reference:
|
[4] C. Chicone: Lyapunov-Schmidt reduction and Melnikov integrals for bifurcation of periodic solutions in coupled oscillators.J. Differ. Equations 112 (1994), 407–447. MR 1293477, 10.1006/jdeq.1994.1110 |
| Reference:
|
[5] C. Chicone: Ordinary Differential Equations with Applications.Springer, New York, 1999. Zbl 0937.34001, MR 1707333 |
| Reference:
|
[6] Ph. Hartman: Ordinary Differential Equations.John Wiley, New York, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[7] M. Y. Li, J. S. Muldowney: Dynamics of differential equations on invariant manifolds.J. Differ. Equations 168 (2000), 295–320. MR 1808452, 10.1006/jdeq.2000.3888 |
| . |
