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2006 | 4 | 2 | 294-303
Tytuł artykułu

A topological invariant for pairs of maps

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we develop the notion of contact orders for pairs of continuous self-maps (f, g) from ℝn, showing that the set Con(f, g) of all possible contact orders between f and g is a topological invariant (we remark that Con(f, id) = Per(f)). As an interesting application of this concept, we give sufficient conditions for the graphs of two continuous self-maps from ℝ intersect each other. We also determine the ordering of the sets Con(f, 0) and Con(f, h), for h ∈ Hom(ℝ) such that f ∘ h = h ∘ f. For this latter set we obtain a generalization of Sharkovsky’s theorem.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
2
Strony
294-303
Opis fizyczny
Daty
wydano
2006-06-01
online
2006-06-01
Twórcy
Bibliografia
  • [1] R. Barton and K. Burns: “A Simple Special Case of Sharkovskii’s Theorem”, Amer. Math. Monthly, Vol. 107(10), (2000), pp. 932–933.
  • [2] N. Bhatia: “New Proof and Extension of Sarkovskii’s Theorem”, Far East J. Math. Sci., Special Volume, Part I, (1996), pp. 53–68.
  • [3] B.-S. Du: “A Simple Proof of Sharkovsky’s Theorem”, Amer. Math. Monthly, Vol. 111(7), (2004), pp. 595–599.
  • [4] S. Elayadi: “On a Converse of Sharkovsky’s Theorem”, Amer. Math. Monthly, Vol. 103, (1996), pp. 386–392.
  • [5] V. Kannan, P.V.S.P. Saradhi and S.P. Seshasai: “A Generalization of Sarkovskii’s Theorem to Higher Dimensions”, J. Nat. Acad. Math. India, Vol. 11, (1997), pp. 69–82.
  • [6] T.-Y. Li and J.A. Yorke: “Period Three Impies Chaos”, Amer. Math. Monthly, Vol. 82(10), (1975), pp. 985–992.
  • [7] V.J. López and L. Snoha: “All Maps of Type 2∞ are Boundary Maps”, Proc. Amer. Math. Soc., Vol. 125(6), (1997), pp. 1667–1673. http://dx.doi.org/10.1090/S0002-9939-97-03452-7
  • [8] M. Polezzi and C. Aniz: “A Šarkovskii-Type Theorem for Pairs of Maps”, Far East J. Dynamical Systems, Vol. 7(1), (2005), pp. 65–75.
  • [9] A.N. Sharkovsky: “Coexistence of cycles of a continuous map of a line into itself”, Ukrain. Mat. Zh., Vol. 16(1), (1964), pp. 61–71 (Russian); Internat. J. Bifur. Chaos Appl. Sci. Engrg., Vol. 5, (1995), pp. 1263–1273 (English).
  • [10] A.N. Sharkovsky: “On cycles and the structure of a continuous map”, Ukrain. Mat. Zh., Vol. 17(3), (1965), pp. 104–111 (Russian).
  • [11] P.D. Straffin, Jr.: “Periodic Points of Continuous Functions”, Math. Mag., Vol. 51(2), (1978), pp. 99–105.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0009-6
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