Geodesic
A note on the fundamental matrix of variational equations in $\mathbb{R}^3$
Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 411-418

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.2003.133999
Classification : 34C30, 34D10, 37C10, 37E99
Keywords: invariant submanifold; variational equation; moving orthogonal system 
Adamec, Ladislav. A note on the fundamental matrix of variational equations in $\mathbb{R}^3$. Mathematica Bohemica, Tome 128 (2003) no. 4, pp. 411-418. doi: 10.21136/MB.2003.133999
@article{10_21136_MB_2003_133999,
     author = {Adamec, Ladislav},
     title = {A note on the fundamental matrix of variational equations in $\mathbb{R}^3$},
     journal = {Mathematica Bohemica},
     pages = {411--418},
     year = {2003},
     volume = {128},
     number = {4},
     doi = {10.21136/MB.2003.133999},
     mrnumber = {2032478},
     zbl = {1052.37014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.133999/}
}
TY  - JOUR
AU  - Adamec, Ladislav
TI  - A note on the fundamental matrix of variational equations in $\mathbb{R}^3$
JO  - Mathematica Bohemica
PY  - 2003
SP  - 411
EP  - 418
VL  - 128
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.133999/
DO  - 10.21136/MB.2003.133999
LA  - en
ID  - 10_21136_MB_2003_133999
ER  - 
%0 Journal Article
%A Adamec, Ladislav
%T A note on the fundamental matrix of variational equations in $\mathbb{R}^3$
%J Mathematica Bohemica
%D 2003
%P 411-418
%V 128
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.133999/
%R 10.21136/MB.2003.133999
%G en
%F 10_21136_MB_2003_133999

[1] L. Adamec: A note on a generalization of Diliberto’s theorem for certain differential equations of higher dimension. (to appear). | MR | Zbl

[2] I. Agricola, T. Friedrich: Global Analysis. American Mathematical Society, Rode Island, 2002. | MR

[3] C. Chicone: Bifurcation of nonlinear oscillations and frequency entrainment near resonance. SIAM J. Math. Anal. 23 (1992), 1577–1608. | DOI | MR

[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 | MR

[5] C. Chicone: Ordinary Differential Equations with Applications. Springer, New York, 1999. | MR | Zbl

[6] Ph. Hartman: Ordinary Differential Equations. John Wiley, New York, 1964. | MR | Zbl

[7] M. Y. Li, J. S. Muldowney: Dynamics of differential equations on invariant manifolds. J. Differ. Equations 168 (2000), 295–320. | DOI | MR

Cité par Sources :