On Ergodic Transformations with Homogeneous Spectrum
Rokhlin's problem on the existence of an ergodic transformation having a homogeneous spectrum of a finite multiplicity is solved. Katok's question about the spectral multiplicity function of Cartesian powers for a generic transformations is also answered.
Unable to display preview. Download preview PDF.
- 1.A. del Junco, A simple measure-preserving transformation with trivial centralizer. Basic J. Math. 79 (1978), No. 2, 357–362.Google Scholar
- 2.A. B. Katok and A. M. Stepin, Metrical propertys of measure preserving homeomorphisms. (Russian) Math. Surv, 25, (1970), 193–220.Google Scholar
- 3.A. B. Katok, Constructions in ergodic theory. Unpublished lecture notes.Google Scholar
- 4.O. N. Ageev, The spectral type of the rearrangement T α,β. Mat. Sb. 188 (1997), 1119–1152.Google Scholar
- 5.G. R. Goodson and M. Leman'czyk, Transformations conjugate to their inverses have even essential values. Proc. Am. Math. Soc. 124 (1996), 2703–2710.Google Scholar
- 6.A. M. Stepin, Les spectres des systemes dynamique. In: Actes, Congres. Intern. Math. 2 (1970), 941–946.Google Scholar