Periodic points for piecewise monotonic transformations

Abstract

AbstractPeriodic points of piecewise monotonic transformations are investigated using an oriented graph, whose closed paths represent the periodic orbits of the transformation. In the first part it is shown that the inverse of the ζ-function is a kind of characteristic polynomial of this graph, which is a power series if the graph is infinite. In the second part, the sets are determined, which can occur as{withandwhereTis a monotonic mod one transformation.