The spectrum of the kinematic dynamo operator for an ideally conducting fluid | Zendy

Carmen Chicone | Zendy; Yuri Latushkin | Zendy; Stephen Montgomery-Smith | Zendy

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The spectrum of the kinematic dynamo operator for an ideally conducting fluid

Author(s) -

Carmen Chicone,

Yuri Latushkin,

Stephen Montgomery-Smith

Publication year - 1995

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/bf02101239

Subject(s) - dynamo , spectrum (functional analysis) , mathematics , operator (biology) , vector field , manifold (fluid mechanics) , mathematical analysis , kinematics , lyapunov exponent , ergodic theory , flow (mathematics) , pure mathematics , physics , classical mechanics , magnetic field , geometry , quantum mechanics , nonlinear system , mechanical engineering , biochemistry , chemistry , repressor , transcription factor , engineering , gene

The spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact Riemannian manifold are described. We prove that the spectrum of the kinematic dynamo operator is exactly one vertical strip whose boundaries can be determined in terms of the Lyapunov-Oseledets exponents with respect to all ergodic measures for the Eulerian flow. Also, we prove that the spectrum of the corresponding group is obtained from the spectrum of its generator by exponentiation. In particular, the growth bound for the group coincides with the spectral bound for the generator.

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