Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 193-209 Printed March 1, 2006
Seoung Ho Lee, Yeon Soo Yoon Mokwon University, Hannam University
Abstract : The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.