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This article is cited in 48 scientific papers (total in 48 papers)
The behaviour of the ndex of periodic points under iterations of a mapping
I. K. Babenko, S. A. Bogatyi
Abstract:
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.
Received: 13.05.1988
Citation:
I. K. Babenko, S. A. Bogatyi, “The behaviour of the ndex of periodic points under iterations of a mapping”, Izv. Akad. Nauk SSSR Ser. Mat., 55:1 (1991), 3–31; Math. USSR-Izv., 38:1 (1992), 1–26
Linking options:
https://www.mathnet.ru/eng/im1020https://doi.org/10.1070/IM1992v038n01ABEH002185 https://www.mathnet.ru/eng/im/v55/i1/p3
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Abstract page: | 579 | Russian version PDF: | 179 | English version PDF: | 18 | References: | 76 | First page: | 3 |
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