A simple method for constructing non-liouvillian first integrals of autonomous planar systems

Axel Schulze-Halberg

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 987-999
  • ISSN: 0011-4642

Abstract

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We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.

How to cite

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Schulze-Halberg, Axel. "A simple method for constructing non-liouvillian first integrals of autonomous planar systems." Czechoslovak Mathematical Journal 56.3 (2006): 987-999. <http://eudml.org/doc/31085>.

@article{Schulze2006,
abstract = {We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.},
author = {Schulze-Halberg, Axel},
journal = {Czechoslovak Mathematical Journal},
keywords = {planar polynomial systems; Kukles systems; generalized Liénard systems; non-liouvillian first integrals; planar polynomial systems; Kukles systems; generalized Liénard systems; non-Liouvillian first integrals},
language = {eng},
number = {3},
pages = {987-999},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A simple method for constructing non-liouvillian first integrals of autonomous planar systems},
url = {http://eudml.org/doc/31085},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Schulze-Halberg, Axel
TI - A simple method for constructing non-liouvillian first integrals of autonomous planar systems
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 987
EP - 999
AB - We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
LA - eng
KW - planar polynomial systems; Kukles systems; generalized Liénard systems; non-liouvillian first integrals; planar polynomial systems; Kukles systems; generalized Liénard systems; non-Liouvillian first integrals
UR - http://eudml.org/doc/31085
ER -

References

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