Prime flows in topological dynamics
Tóm tắt
We present some results in topological dynamics and number theory. The number-theoretical results are estimates of the rates of convergence of sequences {fx26-1}, wherena is irrational,a is taken mod 1, and 0<β<1. One of these results is used to construct a homorphismT of a compact metric spaceX such that the minimal flow (X, T) had no nontrivial homomorphic images, i.e. is a prime flow. We define an infinite family of such flows, and describe other interesting properties of these flows.
Tài liệu tham khảo
J. Auslander,Regular minimal sets, Trans. Amer. Math. Soc.123 (1966), 469–479.
W. Gottschalk and G. Hedlund,Topological Dynamics, Amer. Math. Soc. Colloquium, Vol. 36, Providence, R.I., 1955.
H. Kesten,On a conjecture of Erdös and Szüsz related to uniform distribution mod 1, Acta. Arith.12 (1966–67), 193–212.
H. Keynes,The structure of weakly-mixing minimal transformation groups, Illinois Journ. Math.15 (1971), 475–490.
K. Petersen, Ph. D. Thesis, Yale, 1969.
K. Peterson and L. Shapiro,Induced flows, Trans. Amer. Math. Soc., to appear.