The Multiplier Group of a Quasiperiodic Flow
As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the $n$-torus, is the determining factor of the structure of its generalized symmetry group. It is conjectured that a quasiperiodic flow...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
01.09.2005
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Subjects | |
Online Access | Get full text |
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Summary: | As an absolute invariant of smooth conjugacy, the multiplier group described
the types of space-time symmetries that the flow has, and for a quasiperiodic
flow on the $n$-torus, is the determining factor of the structure of its
generalized symmetry group. It is conjectured that a quasiperiodic flow is
F-algebraic if and only if its multiplier group is a finite index subgroup of
the group of units in the ring of integers of a real algebraic number field F,
and that a quasiperiodic flow is transcendental if and only if its multiplier
group is {1,-1}. These two conjectures are partially validated for n greater or
equal to 2, and fully validated for n=2. |
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DOI: | 10.48550/arxiv.math/0509023 |