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Mathematics of the USSR-Izvestiya, 1992, Volume 38, Issue 1, Pages 1–26
DOI: https://doi.org/10.1070/IM1992v038n01ABEH002185
(Mi im1020)
 

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
References:
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
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1991, Volume 55, Issue 1, Pages 3–31
Bibliographic databases:
UDC: 515.1
MSC: 55M20, 58F22
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{BabBog91}
\by I.~K.~Babenko, S.~A.~Bogatyi
\paper The behaviour of the ndex of periodic points under iterations of a mapping
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 1
\pages 3--31
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1130026}
\zmath{https://zbmath.org/?q=an:0742.58027}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38....1B}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 1--26
\crossref{https://doi.org/10.1070/IM1992v038n01ABEH002185}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992HG30700001}
Linking options:
  • https://www.mathnet.ru/eng/im1020
  • https://doi.org/10.1070/IM1992v038n01ABEH002185
  • https://www.mathnet.ru/eng/im/v55/i1/p3
  • This publication is cited in the following 48 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:579
    Russian version PDF:179
    English version PDF:18
    References:76
    First page:3
     
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