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.
periodic point class;Nielsen number;Nielsen type number;
Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces, Topology and its Applications, 2012, 159, 18, 3752
P. R. Heath and E. Keppelmann, Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I, Topology Appl. 76 (1997), no. 3, 217-247.
P. R. Heath, R. Piccinini, and C. You, Nielsen-type numbers for periodic points. I, Topological fixed point theory and applications (Tianjin, 1988), 88-106, Lecture Notes in Math., 1411, Springer, Berlin, 1989.
P. R. Heath and C. You, Nielsen-type numbers for periodic points. II, Topology Appl. 43 (1992), no. 3, 219-236.
J. Jezierski, Wecken’s theorem for periodic points, Topology 42 (2003), no. 5, 1101-1124.
B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983.
B. Jiang, Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996), no. 1, 151-185.
B. Jiang, S. H. Lee, and M. H. Woo, Reidemeister orbit sets, Fund. Math. 183 (2004), no. 2, 139-156.