The construction of a universally observable flow on the torus

摘要: We give a description of the construction class dynamical systems on two-dimensional torus which are universally observable, i.e., observable by every continuous nonconstant real-valued function torus. motivated work McMahon (1987) who proved that three-dimensional manifolds with horocycle flow have this property. examine example and able to sufficient conditions for be then construct satisfies these conditions. The proofs involve techniques concepts from topological dynamics, number theory.