A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension

Ladislav Adamec

Applications of Mathematics (2005)

  • Volume: 50, Issue: 2, page 93-101
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Adamec, Ladislav. "A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension." Applications of Mathematics 50.2 (2005): 93-101. <http://eudml.org/doc/33209>.

@article{Adamec2005,
abstract = {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.},
author = {Adamec, Ladislav},
journal = {Applications of Mathematics},
keywords = {Poincaré mapping; variational equation; moving orthogonal system; Poincaré mapping; variational equation; moving orthogonal system},
language = {eng},
number = {2},
pages = {93-101},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension},
url = {http://eudml.org/doc/33209},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Adamec, Ladislav
TI - A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 93
EP - 101
AB - 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.
LA - eng
KW - Poincaré mapping; variational equation; moving orthogonal system; Poincaré mapping; variational equation; moving orthogonal system
UR - http://eudml.org/doc/33209
ER -

References

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  7. Ordinary Differential Equations with Applications, Springer-Verlag, New York, 1999. (1999) Zbl0937.34001MR1707333
  8. On systems of ordinary differential equations. In: Contributions to the Theory of Nonlinear Oscillations, Ann. Math. Stud. 20 (1950), 1–38. (1950) MR0034931
  9. Ordinary Differential Equations, John Wiley & Sons, New York-London-Sydney, 1964. (1964) Zbl0125.32102MR0171038
  10. Ordinary Differential Equations, Elsevier, Amsterdam-Oxford-New York-Tokyo, 1986. (1986) Zbl0667.34002MR0929466
  11. A construction of realizations of perturbations of Poincaré maps, Math. Slovaca 36 (1986), 179–190. (1986) MR0849709
  12. Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris, 1892. (1892) 

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