A NOTE ON NIELSEN TYPE NUMBERS
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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.
Abstract
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.
참고문헌 (7)
- P. R. Heath, "Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I", Topology Appl., 76(3), pp.217~247 (1997)
- P. R. Heath, "Nielsen-type numbers for periodic points. I, Topological fixed point theory and applications (Tianjin, 1988)", Lecture Notes in Math., 통권 : 1411, pp.88~106 (1989), Springer
- P. R. Heath, "Nielsen-type numbers for periodic points. II", Topology Appl., 43(3), pp.219~236 (1992)
- J. Jezierski, "Wecken’s theorem for periodic points", Topology, 42(5), pp.1101~1124 (2003)
- B. Jiang, "Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics", American Mathematical Society, 14 (1983)
- B. Jiang, "Estimation of the number of periodic orbits", Pacific J. Math., 172(1), pp.151~185 (1996)
- B. Jiang, "Reidemeister orbit sets", Fund. Math., 183(2), pp.139~156 (2004)