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It is the fact that the eigenvalues <math>k^{-m}<1</math> that marks this as a dissipative system: for a non-dissipative [[measure-preserving dynamical system]], the eigenvalues of the transfer operator lie on the unit circle.
More generally, this operator also has a continuous spectrum: the Hurwitz zeta function <math>\zeta(s,x)</math> is also an eigenvector, with eigenvalue <math>k^
==Characteristic zero==
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