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1999 | 49 | 1 | 203-221
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Applications of Nielsen theory to dynamics

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.
Słowa kluczowe
Rocznik
Tom
49
Numer
1
Strony
203-221
Opis fizyczny
Daty
wydano
1999
Twórcy
autor
  • Department of Mathematics, Peking University, Beijing 100871, China
Bibliografia
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  • [GN] R. Geoghegan and A. Nicas, Lefschetz trace formulae, zeta functions and torsion in dynamics, in: Nielsen Theory and Dynamical Systems, Ch. McCord (ed.), Contemp. Math. 152, Amer. Math. Soc., Providence, 1993, 141-157; Trace and torsion in the theory of flows, Topology 33 (1994) 683-719.
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  • [J1] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983.
  • [J2] B. Jiang, Periodic orbits on surfaces via Nielsen fixed point theory, in: Topology-Hawaii, K. H. Dovermann (ed.), World Scientific, Singapore, 1992, 101-118.
  • [J3] B. Jiang, Nielsen theory for periodic orbits and applications to dynamical systems, in: Nielsen Theory and Dynamical Systems, Ch. McCord (ed.), Contemp. Math. 152, Amer. Math. Soc., Providence, 1993, 183-202; Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996) 151-185.
  • [J4] B. Jiang, Bounds for fixed points on surfaces, Math. Ann. 311 (1998), 467-479.
  • [JG] B. Jiang and B. Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993) 67-89.
  • [JL] B. Jiang and J. Llibre, Minimal sets of periods for torus maps, Discrete Cont. Dynam. Systems 4 (1998), 301-320.
  • [JW] B. Jiang and S. Wang, Twisted topological invariants associated with representations, in: Topics in Knot Theory, M. E. Bozhüyük (ed.) Kluwer, Dordrecht, 1993, 211-227.
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  • [N1] J. Nielsen, Über die Minimalzahl der Fixpunkte bei den Abbildungstypen der Ringflächen, Math. Ann. 82 (1921) 83-93; also in: Jakob Nielsen: Collected Mathematical Papers, vol. 1, V. L. Hansen (ed.), Birkhäuser, Boston, 1986, 99-109.
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  • [N3] J. Nielsen, Fixpunktfrie afbildninger, Mat. Tidsskr. B (1942) 25-41, reviewed by R. Fox, Math. Reviews 7 (1946), 137; English transl.: Fixed point free mappings, in: Jakob Nielsen: Collected Mathematical Papers, vol. 2, V. L. Hansen (ed.), Birkhäuser, Boston, 1986, 221-232.
  • [R] K. Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936) 586-593.
  • [S] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986) 459-473.
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  • [Wa1] S. Wang, Maximum orders of periodic maps on closed surfaces, Topology Appl. 41 (1991) 255-262.
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  • [W] F. Wecken, Fixpunktklassen, I, Math. Ann. 117 (1941) 659-671; II, 118 (1942) 216-234; III, 118 (1942) 544-577.
  • [Y] C. Y. You, A note on periodic points on tori, Beijing Math. 1 (1995) 224-230.
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Bibliografia
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