Quasiperiodic Flows and Algebraic Number Fields
نویسنده
چکیده
We classify a quasiperiodic flow as either algebraic or transcendental. For an algebraic quasiperiodic flow φ on the n-torus, Tn, we prove that an absolute invariant of the smooth conjugacy class of φ, known as the multiplier group, is a subgroup of the group of units of the ring of integers in a real algebraic number field F of degree n over Q. We also prove that for any real algebraic number field F of degree n over Q, there exists an algebraic quasiperiodic flow on Tn whose multiplier group is exactly the group of units of the ring of integers in F . We support and formulate the conjecture that the multiplier group distinguishes the algebraic quasiperiodic flows from the transcendental ones. AMS (MOS) Subject Classification. 37C55, 37C15, 11R04, 11R27
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Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups
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