Diophantine approximation of the orbits in topological dynamical systems (Q1735346)

The present article deals with topological dynamical systems. The main attention is given to the set of points whose orbit can well approximate a given point infinitely often. A formulation of the main problem is ``a general principle for the shrinking target problem in a topological dynamical system''. The authors note that one of the main goals of this paper is to find a general principle for the topological entropy about the topological version of the shrinking target problem in systems as general as possible. It is shown that if a system \((X; T)\) satisfies the specification property, then the entropy transference principle holds true. Here \((X; T)\) is a compact metric space and \(T : X \to X\) is a continuous transformation on \(X\).