Geodesic
The behaviour of the ndex of periodic points under iterations of a mapping
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 1-26.

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This paper strengthens a theorem due to A. Dold on the algebraic properties of sequences of integers which are Lefschetz numbers of the iterates of a continuous map from a finite polyhedron to itself. The realizability of sequences satisfying Dold's condition at a single fixed point of a continuous map on $\mathbf R^3$ is proved. Indices of a fixed point (under iteration) are investigated in the case of a smooth mapping. A linear lower bound on the number of periodic points of a smooth map, which strengthens a result of Shub and Sullivan, is obtained. 
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I. K. Babenko; S. A. Bogatyi. The behaviour of the ndex of periodic points under iterations of a mapping. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 1-26. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a0/

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