zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Lie point symmetries for systems of second order linear ordinary differential equations. (English) Zbl 0649.34018
Recently it was shown that some nonlinear second order differential equations could be linearized by a point transformation generated by the generator G=τ/t+η/x, where τ=τ(x,t), η=η(x,t) are unknown coefficients. Because the set of all generators of a differential equation creates a Lie algebra under the operation of the Lie bracket it is interest in finding the number of generators for a system of differential equations. The paper in the heading deals with the mentioned problem for the system x '' =ax+by, y '' =cx+dy, where a,b,c,d are constant coefficients. Some considerations are extended to higher dimensional systems. The case when a,b,c,d depend upon t is also discussed.
Reviewer: J.Banás
34A30Linear ODE and systems, general
22E60Lie algebras of Lie groups
17B15Representations of Lie algebras, analytic theory