Abstract
The pilgerschritt transform is an iterative method which can be used to calculate one-parameter subgroups of groups of matrices, whose restrictions to the interval [0,1] belongs to a given homotopy class. The restrictions of one-parameter subgroups are fixed points of this method. All fixed points can be described by a product integral equation. Until now there could be shown for special groups of matrices that these fixed points are attractive. This paper deals with the group Aff(1,ℝ), where the product integral equation can be reduced to a Fredholm integral equation of the second kind. In this case the existence of one-parameter subgroups is proved, whose restrictions are not attractive fixed points. Furthermore, the existence of other fixed points is shown.
Presented by N. Netzer
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© 1985 Springer-Verlag
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Förg-Rob, W., Netzer, N. (1985). Product-integration and one-parameter subgroups of linear lie-groups. In: Liedl, R., Reich, L., Targonski, G. (eds) Iteration Theory and its Functional Equations. Lecture Notes in Mathematics, vol 1163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076419
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DOI: https://doi.org/10.1007/BFb0076419
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