Linear flows on \(\kappa\)-solenoids (Q1296278)

The author defines families of linear flows on the inverse limits of \(n\)-dimensional tori \(T^n\) (\(n\) fixed) and proves that two flows from such a family are topologically equivalent if and only if there is an automorphism generating the equivalence. This result generalizes the well-known result in the case \(n=2\). Moreover the author gives a characterization of the automorphism on the finite product of 1D solenoids and works out the 2D case in detail. He presents a condition on the character group of a finite-dimensional inverse limit that determines when the inverse limit is isomorphic with a product of one-dimensional solenoids. As an application the author obtains that any two (topologically) equivalent almost periodic flows are equivalent to members of the same family of irrational linear flows, and so the results of the author serve as a program for the classification of almost periodic flows in complete metric spaces.