A conjecture of Renshaw and Mote concerning gyroscopic systems
with parameters predicts the eigenvalue locus in the neighbourhood
of a double zero eigenvalue. In the present paper this conjecture
is reformulated in the language of generalized eigenvectors,
angular splitting and analytic behaviour of eigenvalues. Two
counter-examples for systems of dimension two show that the
conjecture is not generally true. Finally, splitting or analytic
behaviour of eigenvalues is characterized in terms of expansion of
the eigenvalues in fractional powers of the parameter.

Number of pages | 6 |
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Publication status | Published - 1997 |
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