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

Applications of Mathematics (2005)

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

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topAdamec, 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

top- 10.1023/A:1023016529118, Appl. Math. 42 (1997), 293–309. (1997) Zbl0903.34043MR1453934DOI10.1023/A:1023016529118
- A note on the transition mapping for $n$-dimensional systems, , Submitted.
- Global Analysis, American Mathematical Society, Rhode Island, 2002. (2002) MR1998826
- On the multivalued Poincaré operators, Topol. Meth. Nonlin. Anal. 10 (1997), 171–182. (1997) Zbl0909.47038MR1646627
- 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. (2002)
- Theory of Bifurcation of Dynamical System on the Plane, John Wiley & Sons, New York-London-Sydney, 1973. (1973)
- Ordinary Differential Equations with Applications, Springer-Verlag, New York, 1999. (1999) Zbl0937.34001MR1707333
- On systems of ordinary differential equations. In: Contributions to the Theory of Nonlinear Oscillations, Ann. Math. Stud. 20 (1950), 1–38. (1950) MR0034931
- Ordinary Differential Equations, John Wiley & Sons, New York-London-Sydney, 1964. (1964) Zbl0125.32102MR0171038
- Ordinary Differential Equations, Elsevier, Amsterdam-Oxford-New York-Tokyo, 1986. (1986) Zbl0667.34002MR0929466
- A construction of realizations of perturbations of Poincaré maps, Math. Slovaca 36 (1986), 179–190. (1986) MR0849709
- Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris, 1892. (1892)

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