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Lipschitz conjugacy of linear flows
Author(s) -
Kawan C.,
Stender T.
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdp034
Subject(s) - lipschitz continuity , conjugacy class , mathematics , eigenvalues and eigenvectors , lipschitz domain , simple (philosophy) , pure mathematics , conjugate , mathematical analysis , physics , philosophy , epistemology , quantum mechanics
In this paper, we characterize Lipschitz conjugacy of linear flows on ℝ d 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.