| Title:
|
A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension (English) |
| Author:
|
Adamec, Ladislav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
93-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension. (English) |
| Keyword:
|
Poincaré mapping |
| Keyword:
|
variational equation |
| Keyword:
|
moving orthogonal system |
| MSC:
|
34C05 |
| MSC:
|
34C30 |
| MSC:
|
34D10 |
| MSC:
|
37E99 |
| idZBL:
|
Zbl 1099.37032 |
| idMR:
|
MR2125152 |
| DOI:
|
10.1007/s10492-005-0006-2 |
| . |
| Date available:
|
2009-09-22T18:21:00Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134594 |
| . |
| Reference:
|
[1] L. Adamec: Kinetical systems.Appl. Math. 42 (1997), 293–309. Zbl 0903.34043, MR 1453934, 10.1023/A:1023016529118 |
| Reference:
|
[2] L. Adamec: A note on the transition mapping for $n$-dimensional systems., Submitted. |
| Reference:
|
[3] I. Agricola, T. Friedrich: Global Analysis.American Mathematical Society, Rhode Island, 2002. MR 1998826 |
| Reference:
|
[4] J. Andres: On the multivalued Poincaré operators.Topol. Meth. Nonlin. Anal. 10 (1997), 171–182. Zbl 0909.47038, MR 1646627, 10.12775/TMNA.1997.027 |
| Reference:
|
[5] J. Andres: Poincarés translation multioperator revisted. In: Proceedings of the 3rd Polish Symposium of Nonlinear Analalysis, Łódź, January 29–31, 2001.Lecture Notes Nonlinear Anal. 3 (2002), 7–22. |
| Reference:
|
[6] A. A. Andronov, E. A. Leontovich, I. I. Gordon, and I. I. Mayer: Theory of Bifurcation of Dynamical System on the Plane.John Wiley & Sons, New York-London-Sydney, 1973. |
| Reference:
|
[7] C. Chicone: Ordinary Differential Equations with Applications.Springer-Verlag, New York, 1999. Zbl 0937.34001, MR 1707333 |
| Reference:
|
[8] S. P. Diliberto: On systems of ordinary differential equations. In: Contributions to the Theory of Nonlinear Oscillations.Ann. Math. Stud. 20 (1950), 1–38. MR 0034931 |
| Reference:
|
[9] P. Hartman: Ordinary Differential Equations.John Wiley & Sons, New York-London-Sydney, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[10] J. Kurzweil: Ordinary Differential Equations.Elsevier, Amsterdam-Oxford-New York-Tokyo, 1986. Zbl 0667.34002, MR 0929466 |
| Reference:
|
[11] M. Medveď: A construction of realizations of perturbations of Poincaré maps.Math. Slovaca 36 (1986), 179–190. MR 0849709 |
| Reference:
|
[12] H. Poincaré: Les méthodes nouvelles de la mécanique céleste.Gauthier-Villars, Paris, 1892. |
| . |
