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Journal of the London Mathematical Society Advance Access originally published online on October 8, 2009
Journal of the London Mathematical Society 2009 80(3):699-715; doi:10.1112/jlms/jdp034
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© 2009 London Mathematical Society

Lipschitz conjugacy of linear flows

C. Kawan

Institut für Mathematik
Universität Augsburg
Universitätsstrasse 14
86135 Augsburg
Germany
christoph.kawan@math.uni-augsburg.de

T. Stender

Institut für Mathematik
Universität Augsburg
Universitätsstrasse 14
86135 Augsburg
Germany

In this paper, we characterize Lipschitz conjugacy of linear flows on Rd algebraically. We show that two hyperbolic linear flows are Lipschitz conjugate if and only if the Jordan forms of the system matrices are the same except for the simple Jordan blocks where the imaginary parts of the eigenvalues may differ. Using a well-known result of Kuiper we obtain a characterization of Lipschitz conjugacy for arbitrary linear flows.

2000 Mathematics Subject Classification 34A30.

Received March 20, 2008; published online October 8, 2009.


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