Communications of the
Korean Mathematical Society CKMS

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

Keywords: periodic point class, Nielsen number, Nielsen type number

MSC numbers: Primary 55M20, 57N99