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Session 35. Topological fixed point theory and related topics
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The Nielsen numbers of iterations of maps on infra-solvmanifolds of type \(\mathrm{(R)}\) and periodic points |
Jong Bum Lee, Sogang University, Korea
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The talk is based on the joint work with A. Fel'shtyn, [2]
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Utilizing the arguments employed mainly in [1] and [3] for the Lefschetz numbers of iterations, we study the asymptotic behavior of the sequence of the Nielsen
numbers \(\{N(f^k)\}\), the {essential periodic orbits} of \(f\) and the homotopy minimal periods of \(f\) by using the Nielsen theory of maps \(f\) on
infra-solvmanifolds of type \(\mathrm{(R)}\).
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References-
I. K. Babenko and S. A. Bogatyĭ,
The behavior of the index of periodic points under iterations of a mapping,
Izv. Akad. Nauk SSSR Ser. Mat., 55 (1991), 3-31 (Russian);
translation in Math. USSR-Izv., 38 (1992), 1-26.
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A. Fel'shtyn and J. B. Lee,
The Nielsen numbers of iterations of maps on infra-solvmanifolds of type \(\mathrm{(R)}\) and periodic points,
arXiv:1403.7631.
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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.
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