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Self-maps on flat manifolds with infinitely many periods
| 1. | Department of Mathematics, Capital Normal University, Beijing 100048, Beijing International Center for Mathematical Research, China |
| 2. | Department of Mathematics & Institute of mathematics and interdisciplinary science, Capital Normal University, Beijing 100048, China |
References:
| [1] |
L. Alsedà, S. Baldwin, J. Llibre, R. Swanson and W. Szlenk, Minimal sets of periods for torus maps via Nielsen numbers, Pacific J. Math., 169 (1995), 1-32. |
| [2] |
L. Block, J. Guckenheimer, M. Misiurewicz and L. Young, Periodic points and topological entropy of one-dimensional maps, in "Global Theory of Dynamical Systems" (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Math., 819, Springer, Berlin, (1980), 18-34. |
| [3] |
L. Charlap, "Bieberbach Groups and Flat Manifolds," Universitext, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4613-8687-2. |
| [4] |
J. Jezierski, Wecken's theorem for periodic points in dimension at least $3$, Topology and its Applications, 153 (2006), 1825-1837.
doi: 10.1016/j.topol.2005.06.008. |
| [5] |
J. Jezierski, E. Keppelmann and W. Marzantowicz, Wecken property for periodic points on the Klein bottle, Topol. Methods Nonlinear Anal., 33 (2009), 51-64. |
| [6] |
B. Jiang, "Lectures on Nielsen Fixed Point Theory," Contemporary Mathematics, 14, American Mathematical Society, Providence, R.I., 1983. |
| [7] |
B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Contin. Dynam. Systems, 4 (1998), 301-320.
doi: 10.3934/dcds.1998.4.301. |
| [8] |
J. Jezierski and W. Marzantowicz, "Homotopy Methods in Topological Fixed and Periodic Points Theory," Topological Fixed Point Theory and Its Applications, 3, Springer, Dordrecht, 2006. |
| [9] |
J. Y. Kim, S. S. Kim and X. Zhao, Minimal sets of periods for maps on the Klein bottle, J. Korean Math. Soc., 45 (2008), 883-902.
doi: 10.4134/JKMS.2008.45.3.883. |
| [10] |
S. W. Kim, J. B. Lee and K. B. Lee, Averaging formula for Nielsen numbers, Nagoya Math. J., 178 (2005), 37-53. |
| [11] |
K. B. Lee, Maps on infra-nilmanifolds, Pacific J. Math., 168 (1995), 157-166. |
| [12] |
J. B. Lee and K. B. Lee, Lefschetz numbers for continuous maps, and periods for expanding maps on infra-nilmanifolds, J. Geom. Phys., 56 (2006), 2011-2023.
doi: 10.1016/j.geomphys.2005.11.003. |
| [13] |
J. B. Lee and X. Zhao, Homotopy minimal periods for expanding maps on infra-nilmanifolds, J. Math. Soc. Japan, 59 (2007), 179-184.
doi: 10.2969/jmsj/1180135506. |
| [14] |
J. Llibre, A note on the set of periods for Klein bottle maps, Pacific J. Math., 157 (1993), 87-93. |
| [15] |
R. Tauraso, Sets of periods for expanding maps on flat manifolds, Monatshefte für Mathematik, 128 (1999), 151-157.
doi: 10.1007/s006050050052. |
show all references
References:
| [1] |
L. Alsedà, S. Baldwin, J. Llibre, R. Swanson and W. Szlenk, Minimal sets of periods for torus maps via Nielsen numbers, Pacific J. Math., 169 (1995), 1-32. |
| [2] |
L. Block, J. Guckenheimer, M. Misiurewicz and L. Young, Periodic points and topological entropy of one-dimensional maps, in "Global Theory of Dynamical Systems" (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Math., 819, Springer, Berlin, (1980), 18-34. |
| [3] |
L. Charlap, "Bieberbach Groups and Flat Manifolds," Universitext, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4613-8687-2. |
| [4] |
J. Jezierski, Wecken's theorem for periodic points in dimension at least $3$, Topology and its Applications, 153 (2006), 1825-1837.
doi: 10.1016/j.topol.2005.06.008. |
| [5] |
J. Jezierski, E. Keppelmann and W. Marzantowicz, Wecken property for periodic points on the Klein bottle, Topol. Methods Nonlinear Anal., 33 (2009), 51-64. |
| [6] |
B. Jiang, "Lectures on Nielsen Fixed Point Theory," Contemporary Mathematics, 14, American Mathematical Society, Providence, R.I., 1983. |
| [7] |
B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Contin. Dynam. Systems, 4 (1998), 301-320.
doi: 10.3934/dcds.1998.4.301. |
| [8] |
J. Jezierski and W. Marzantowicz, "Homotopy Methods in Topological Fixed and Periodic Points Theory," Topological Fixed Point Theory and Its Applications, 3, Springer, Dordrecht, 2006. |
| [9] |
J. Y. Kim, S. S. Kim and X. Zhao, Minimal sets of periods for maps on the Klein bottle, J. Korean Math. Soc., 45 (2008), 883-902.
doi: 10.4134/JKMS.2008.45.3.883. |
| [10] |
S. W. Kim, J. B. Lee and K. B. Lee, Averaging formula for Nielsen numbers, Nagoya Math. J., 178 (2005), 37-53. |
| [11] |
K. B. Lee, Maps on infra-nilmanifolds, Pacific J. Math., 168 (1995), 157-166. |
| [12] |
J. B. Lee and K. B. Lee, Lefschetz numbers for continuous maps, and periods for expanding maps on infra-nilmanifolds, J. Geom. Phys., 56 (2006), 2011-2023.
doi: 10.1016/j.geomphys.2005.11.003. |
| [13] |
J. B. Lee and X. Zhao, Homotopy minimal periods for expanding maps on infra-nilmanifolds, J. Math. Soc. Japan, 59 (2007), 179-184.
doi: 10.2969/jmsj/1180135506. |
| [14] |
J. Llibre, A note on the set of periods for Klein bottle maps, Pacific J. Math., 157 (1993), 87-93. |
| [15] |
R. Tauraso, Sets of periods for expanding maps on flat manifolds, Monatshefte für Mathematik, 128 (1999), 151-157.
doi: 10.1007/s006050050052. |
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