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Paper   IPM / M / 15100
School of Mathematics
  Title:   Orbit equivalence of Cantor minimal systems and their continuous spectra
  Author(s):  Maryam Hosseini (Joint with T. Giordano and D. Handelman)
  Status:   Published
  Journal: Math. Z.
  Vol.:  289
  Year:  2018
  Pages:   1199-1218
  Supported by:  IPM
To any continuous eigenvalue of a Cantor minimal system (XT), we associate an element of the dimension group K0(XT) associated to (XT). We introduce and study the concept of irrational miscibility of a dimension group. The main property of these dimension groups is the absence of irrational values in the additive group of continuous spectrum of their realizations by Cantor minimal systems. The strong orbit equivalence (respectively orbit equivalence) class of a Cantor minimal system associated to an irrationally miscible dimension group (Gu) (resp. with trivial infinitesimal subgroup) with trivial rational subgroup, have no non-trivial continuous eigenvalues.

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