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2000 | 163 | 2 | 99-115
Tytuł artykułu

Minimal periods of maps of rational exterior spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of description of the set Per(f) of all minimal periods of a self-map f:X → X is studied. If X is a rational exterior space (e.g. a compact Lie group) then there exists a description of the set of minimal periods analogous to that for a torus map given by Jiang and Llibre. Our approach is based on the Haibao formula for the Lefschetz number of a self-map of a rational exterior space.
Rocznik
Tom
163
Numer
2
Strony
99-115
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-06-15
poprawiono
1999-11-26
Twórcy
  • <AFILIACJE>Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, G. Narutowicza 11/12, 80-952 Gdańsk, graff@mif.pg.gda.pl
Bibliografia
  • [BB] I. K. Babenko and C. A. Bogatyĭ, The behaviour of the index of periodic points under iterations of a mapping, Math. USSR-Izv. 38 (1992), 1-26.
  • [BM] P. E. Blanksby and H. L. Montgomery, Algebraic integers near the unit circle, Acta Arith. 18 (1971), 355-369.
  • [CLN] J. Casasayas, J. Llibre and A. Nunes, Periodic orbits of transversal maps, Math. Proc. Cambridge Philos. Soc. 118 (1995), 161-181.
  • [Ch] K. Chandrasekharan, Introduction to Analytic Number Theory, Springer, Berlin, 1968.
  • [CMPY] S. N. Chow, J. Mallet-Paret and J. A. Yorke, A bifurcation invariant: Degenerate orbits treated as a cluster of simple orbits, in: Geometric Dynamics (Rio de Janeiro 1981), Lecture Notes in Math. 1007, Springer, 1983, 109-131.
  • [D] A. Dold, Fixed point indices of iterated maps, Invent. Math. 74 (1985), 419-435.
  • [H] D. Haibao, The Lefschetz number of iterated maps, Topology Appl. 67 (1995), 71-79.
  • [JM] J. Jezierski and W. Marzantowicz, Minimal periods for nilmanifolds, Preprint No 67, Faculty of Mathematics and Informatics UAM, June 1997.
  • [JL] B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Contin. Dynam. Systems 4 (1998), 301-320.
  • [Mats] T. Matsuoka, The number of periodic points of smooth maps, Ergodic Theory Dynam. Systems 9 (1989), 153-163.
  • [M] W. Marzantowicz, Determination of the periodic points of smooth mappings using Lefschetz numbers and their powers, Russian Math. Izv. 41 (1997), 80-89.
  • [MP] W. Marzantowicz and P. Przygodzki, Finding periodic points of a map by use of a k-adic expansion, Discrete Contin. Dynam. Systems 5 (1999), 495-514.
  • [N] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, PWN, Warszawa, 1974.
  • [Sch] A. Schinzel, Primitive divisors of the expression $A^n-B^n$ in algebraic number fields, J. Reine Angew. Math. 268/269 (1974), 27-33.
  • [SS] M. Shub and P. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps, Topology 13 (1974), 189-191.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv163i2p99bwm
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