Rigidity of projective conjugacy for quasiperiodic flows of Koch type

Lennard F. Bakker¹

¹ Department of Mathematics Brigham Young University 292 Talmage Math//Computer Building P.O. Box 26539 Provo, UT 84602-6539, U.S.A.

Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 291-312

Résumé

For quasiperiodic flows of Koch type, we exploit an algebraic rigidity of an equivalence relation on flows, called projective conjugacy, to algebraically characterize the deviations from completeness of an absolute invariant of projective conjugacy, called the multiplier group, which describes the generalized symmetries of the flow. We then describe three ways by which two quasiperiodic flows with the same Koch field are projectively conjugate when their multiplier groups are identical. The first way involves a quantity introduced here, called the $G$-paragon class number of the multiplier group. The second involves the generalized Bowen–Franks groups and the class number of an order. The third involves conjugacy of the actions of the multiplier group by commuting toral automorphisms, for which one of these actions is irreducible, and a condition introduced here, called PCF, on the common real eigenvectors of the irreducible action. Additionally, we describe two ways by which similiar actions of the multiplier group can fail to be conjugate.

Détail

DOI : 10.4064/cm112-2-6

Keywords: quasiperiodic flows koch type exploit algebraic rigidity equivalence relation flows called projective conjugacy algebraically characterize deviations completeness absolute invariant projective conjugacy called multiplier group which describes generalized symmetries flow describe three ways which quasiperiodic flows koch field projectively conjugate their multiplier groups identical first involves quantity introduced here called g paragon class number multiplier group second involves generalized bowen franks groups class number order third involves conjugacy actions multiplier group commuting toral automorphisms which these actions irreducible condition introduced here called pcf common real eigenvectors irreducible action additionally describe ways which similiar actions multiplier group fail conjugate