논문KCI 등재
Minimal sets of periods for maps on the Klein bottle
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초록
The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.
Abstract
The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.
참고문헌 (9)
- L. Alseda, "Minimal sets of periods for torus maps via Nielsen numbers", Pacific Journal of Mathematics, 169(1), pp.1~32 (1995)
- B. Halpern, "Periodic points on Klein bottle, unpublished", ~
- B. Jiang, "Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics", pp.14~ (1983), American Mathematical Society
- B. Jiang, "Minimal sets of periods for torus maps", Discrete and Continuous Dynamical Systems, 4(2), pp.301~320 (1998)
- J. Jezierski, "Homotopy minimal periods for nilmanifold maps", Mathematische Zeitschrift, 239(2), pp.381~414 (2002)
- S. Kwasik, "The Nielsen numbers of homotopically periodic maps of infranilmanifolds", Journal of the London Mathematical Society, 38(3), pp.544~554 (1988)
- S. W. Kim, "Averaging formula for Nielsen numbers", Nagoya Mathematics Journal, 178, pp.37~53 (2005)
- K. B. Lee, "Maps on infra-nilmanifolds", Pacific Journal of Mathematics, 168(1), pp.157~166 (1995)
- J. Llibre, "A note on the set of periods for Klein bottle maps", Pacific Journal of Mathematics, 157(1), pp.87~93 (1993)
관련 논문AI추천
Computation of the Nielsen type numbers for maps on the Klein bottle김현중, 유원석, 이종범대한수학회 · 대한수학회지2008 · 제45권 제5호Homotopy minimal periods of maps on the Klein bottle이종범대한수학회 · 대한수학회논문집2018 · 제33권 제3호A NOTE ON NIELSEN TYPE NUMBERS이승호대한수학회 · 대한수학회논문집2010 · 제25권 제2호A Nielsen type number of fibre preserving maps김승원, 이승호대한수학회 · 대한수학회논문집2013 · 제28권 제2호A note on the set of root classes이승호대한수학회 · 대한수학회논문집2009 · 제24권 제3호Density of the homotopy minimal periods of maps on infra-solvmanifolds of type $\R$이종범, Xuezhi Zhao대한수학회 · 대한수학회지2018 · 제55권 제2호
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