Planar 2-homogeneous commutative rational vector fields

Simple item page
dc.contributor.authorAlkauskas, Giedrius
dc.date.accessioned2022-02-16T18:17:20Z
dc.date.available2022-02-16T18:17:20Z
dc.date.issued2018-07-03
dc.description.abstractIn this article we prove the following result: if two 2-dimensional 2-homogeneous rational vector fields commute, then either both vector fields can be explicitly integrated to produce rational flows with orbits being lines through the origin, or both flows can be explicitly integrated in terms of algebraic functions. In the latter case, orbits of each flow are given in terms of 1-homogeneous rational functions W as curves W(x,y)=const. An exhaustive method to construct such commuting algebraic flows is presented. The degree of the so-obtained algebraic functions in two variables can be arbitrarily high.
dc.description.departmentMathematics
dc.formatText
dc.format.extent21 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAlkauskas, G. (2018). Planar 2-homogeneous commutative rational vector fields. <i>Electronic Journal of Differential Equations, 2018</i>(138), pp. 1-21.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15338
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectTranslation equation
dc.subjectFlow
dc.subjectRational vector fields
dc.subjectLinear ODEs
dc.subjectAutonomous non-linear ODEs
dc.subjectFirst order linear PDEs
dc.subjectAlgebraic functions
dc.subjectLie bracket
dc.subjectCommuting flows
dc.subjectCremona groups
dc.subjectWronskian
dc.titlePlanar 2-homogeneous commutative rational vector fields
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
alkauskas.pdf
Size:
326.48 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Journal of Differential Equations