Dense orbits of rationals
Author: Michael D. Boshernitzan
Journal: Proc. Amer. Math. Soc. 117 (1993), 1201-1203
MSC: Primary 58F08
MathSciNet review: 1134622
Abstract: Let denote the rational points of the interval . We construct a one-to-one piecewise linear map which has the following properties:
(1) for any if and only if ;
(2) all the orbits , are dense in ;
(3) is an automorphism of the unit circle .
This example is motivated by a question of Friedman who was interested, because of an application to logic (Dynamic Recursion Theory), in an example of a piecewise polynomial map having an orbit that is dense in and lies in (for some ).
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