Minimal periods of maps of rational exterior spaces
Graff, Grzegorz
Fundamenta Mathematicae, Tome 163 (2000), p. 99-115 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212438 
@article{bwmeta1.element.bwnjournal-article-fmv163i2p99bwm,
     author = {Grzegorz Graff},
     title = {Minimal periods of maps of rational exterior spaces},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {99-115},
     zbl = {0969.37011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv163i2p99bwm}
}

Graff, Grzegorz. Minimal periods of maps of rational exterior spaces. Fundamenta Mathematicae, Tome 163 (2000) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i2p99bwm/

[00000] [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.

[00001] [BM] P. E. Blanksby and H. L. Montgomery, Algebraic integers near the unit circle, Acta Arith. 18 (1971), 355-369. | Zbl 0221.12003

[00002] [CLN] J. Casasayas, J. Llibre and A. Nunes, Periodic orbits of transversal maps, Math. Proc. Cambridge Philos. Soc. 118 (1995), 161-181. | Zbl 0839.58044

[00003] [Ch] K. Chandrasekharan, Introduction to Analytic Number Theory, Springer, Berlin, 1968. | Zbl 0169.37502

[00004] [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.

[00005] [D] A. Dold, Fixed point indices of iterated maps, Invent. Math. 74 (1985), 419-435. | Zbl 0583.55001

[00006] [H] D. Haibao, The Lefschetz number of iterated maps, Topology Appl. 67 (1995), 71-79. | Zbl 0836.55001

[00007] [JM] J. Jezierski and W. Marzantowicz, Minimal periods for nilmanifolds, Preprint No 67, Faculty of Mathematics and Informatics UAM, June 1997.

[00008] [JL] B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Contin. Dynam. Systems 4 (1998), 301-320. | Zbl 0965.37019

[00009] [Mats] T. Matsuoka, The number of periodic points of smooth maps, Ergodic Theory Dynam. Systems 9 (1989), 153-163.

[00010] [M] W. Marzantowicz, Determination of the periodic points of smooth mappings using Lefschetz numbers and their powers, Russian Math. Izv. 41 (1997), 80-89.

[00011] [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. | Zbl 0965.37015

[00012] [N] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, PWN, Warszawa, 1974. | Zbl 0276.12002

[00013] [Sch] A. Schinzel, Primitive divisors of the expression An-Bn in algebraic number fields, J. Reine Angew. Math. 268/269 (1974), 27-33. | Zbl 0287.12014

[00014] [SS] M. Shub and P. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps, Topology 13 (1974), 189-191. | Zbl 0291.58014