Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems. (English) Zbl 1095.54016

Bressaud, Xavier; Durand, Fabien; Maass, Alejandro

J. Lond. Math. Soc., II. Ser. 72, No. 3, 799-816 (2005).

Results from M. I. Cortez, F. Durand, B. Host, and A. Maass [J. Lond. Math. Soc., II. Ser. 67, No. 3, 790–804 (2003; Zbl 1045.54011)] are strengthened here: necessary and sufficient conditions are given for the so-called linearly recurrent Cantor dynamical systems to have measurable and continuous eigenfunctions. Also an example of a linearly recurrent system with a nontrivial Kronecker factor and a trivial maximal equicontinuous factor is constructed explicitly.

Reviewer: Ľubomír Snoha (Banská Bystrica)

MSC:

54H20	Topological dynamics (MSC2010)
37B20	Notions of recurrence and recurrent behavior in topological dynamical systems

Keywords:

linearly recurrent Cantor dynamical system; Kakutani-Rokhlin partition; eigenvalue; nontrivial Kronecker factor; maximal equicontinuous factor

Citations:

Zbl 1045.54011