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2003, 2003(Special): 68-77. doi: 10.3934/proc.2003.2003.68

A reducible representation of the generalized symmetry group of a quasiperiodic flow

L. Bakker 1,

1. 

Department of Mathematics, Brigham Young University, Provo, UT 84602

Received  June 2002 Published  April 2003

The generalized symmetry group of a quasiperiodic flow on a $n$-torus is the group theoretic normalizer, within the group of diffeomorphisms of the $n$-torus, of the one parameter abelian group of diffeomorphisms generated by the flow. Up to conjugacy, the generalized symmetry group of a quasiperiodic flow is determined by a system of uncoupled first order partial differential equations. New types of symmetries (other than the classical types of symmetries or time-reversing symmetries) may exist depending on certain algebraic relationships being satisfied by pair wise ratios of the frequencies of the quasiperiodic flow. These new symmetries, when they exist, are a dominant feature of a reducible linear representation of the generalized symmetry group in the de Rham cohomology of the $n$-torus.
Keywords: Quasiperiodic Flow, Generalized Symmetry, Linear Representation..
Mathematics Subject Classification: Primary: 20C99, 58F27; Secondary: 12F0.
Citation: L. Bakker. A reducible representation of the generalized symmetry group of a quasiperiodic flow. Conference Publications, 2003, 2003 (Special) : 68-77. doi: 10.3934/proc.2003.2003.68
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