A relative Reidemeister orbit number
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.
Keywords : Reidemeister sets, relative Reidemeister orbit numbers, Nielsen type relative essential $n$-orbit numbers
MSC numbers : Primary 55M20, 54H25
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