대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권3호
  • /
  • Pages.883-902
  • /
  • 2008
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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MINIMAL SETS OF PERIODS FOR MAPS ON THE KLEIN BOTTLE

  • Kim, Ju-Young (Department of Mathematics Catholic University of Daegu) ;
  • Kim, Sung-Sook (Department of Applied Mathematics Paichai University) ;
  • Zhao, Xuezhi (Department of Mathematics Capital Normal University)
  • 발행 : 2008.05.31
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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.

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참고문헌

  1. L. Alseda, S. Baldwin, J. Llibre, R. Swanson, and W. Szlenk, Minimal sets of periods for torus maps via Nielsen numbers, Pacific J. Math. 169 (1995), no. 1, 1-32 https://doi.org/10.2140/pjm.1995.169.1
  2. B. Halpern, Periodic points on Klein bottle, unpublished
  3. B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983
  4. B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Contin. Dynam. Systems 4 (1998), no. 2, 301-320 https://doi.org/10.3934/dcds.1998.4.301
  5. J. Jezierski and W. Marzantowicz, Homotopy minimal periods for nilmanifold maps, Math. Z. 239 (2002), no. 2, 381-414 https://doi.org/10.1007/s002090100303
  6. S. Kwasik and K. B. Lee, The Nielsen numbers of homotopically periodic maps of infranilmanifolds, J. London Math. Soc. (2) 38 (1988), no. 3, 544-554
  7. S. W. Kim, J. B. Lee, and K. B. Lee, Averaging formula for Nielsen numbers, Nagoya Math. J. 178 (2005), 37-53 https://doi.org/10.1017/S0027763000009107
  8. K. B. Lee, Maps on infra-nilmanifolds, Pacific J. Math. 168 (1995), no. 1, 157-166 https://doi.org/10.2140/pjm.1995.168.157
  9. J. Llibre, A note on the set of periods for Klein bottle maps, Pacific J. Math. 157 (1993), no. 1, 87-93 https://doi.org/10.2140/pjm.1993.157.87

피인용 문헌

  1. Homotopical theory of periodic points of periodic homeomorphisms on closed surfaces vol.156, pp.15, 2009, https://doi.org/10.1016/j.topol.2009.07.012
  2. Self-maps on flat manifolds with infinitely many periods vol.32, pp.6, 2012, https://doi.org/10.3934/dcds.2012.32.2223