Abstract
There are two algebraic lower bounds of the number of n-periodic points of a self-map \({f : M \rightarrow M}\) of a compact smooth manifold of dimension at least 3:
and
In general NJD n (f) may be much greater than NF n (f). In the simply connected case, the equality of the two numbers is equivalent to the sequence of Lefschetz numbers satisfying restrictions introduced by Chow, Mallet-Parret and Yorke (1983). The last condition is not sufficient in the non-simply connected case. Here we give some conditions which guarantee the equality when \({\pi_{1}M = \mathbb{Z}_{2}}\).
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Jezierski, J. A sufficient condition for the realizability of the least number of periodic points of a smooth map. J. Fixed Point Theory Appl. 18, 609–626 (2016). https://doi.org/10.1007/s11784-016-0311-2
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DOI: https://doi.org/10.1007/s11784-016-0311-2