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Stationary groups of linear differential equations. (English) Zbl 0573.34028
Let $$G(P_ n)$$ be a stationary group formed by all global transformations of the form $$<c| h''|^{(1-n)/2},h>$$, where $$c\neq 0$$ and $$h(I)=I$$, $$h\in C^{n+1}(I)$$, h’(x)$$\neq 0$$ on I, that globally transform n-order (n$$\geq 2)$$ linear differential equation $$P_ n$$ into itself. For each group $$G(P_ n)$$ the set of all h occurring in its elements forms the group $$G_ 0(P_ n)$$ with respect to composition.
The author lists all possible groups $$G_ 0(P_ n)$$ up to $$C^{n+1}$$- conjugacy, discusses the oscillatory properties for the equation $$P_ n$$ if it is iterated from a second order linear differential equation. Moreover he presents all cases when $$G_ 0(P_ n)$$ is $$C^{n+1}$$ conjugate and specifies 5 possible types of subgroups of increasing elements of $$G_ 0(P_ n)$$ with respect to the number of parameters.
Reviewer: D.Bobrowski

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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