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1998 | 156 | 1 | 33-66
Tytuł artykułu

X-minimal patterns and a generalization of Sharkovskiĭ's theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the law of coexistence of different types of cycles for a continuous map of the interval. For this we introduce the notion of eccentricity of a pattern and characterize those patterns with a given eccentricity that are simplest from the point of view of the forcing relation. We call these patterns X-minimal. We obtain a generalization of Sharkovskiĭ's Theorem where the notion of period is replaced by the notion of eccentricity.
Rocznik
Tom
156
Numer
1
Strony
33-66
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-10-24
poprawiono
1997-04-22
Twórcy
autor
autor
  • athematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovak Republic, matekuch@savba.sk
Bibliografia
  • [ALM] L. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Sci., Singapore, 1993.
  • [ALS] L. Alsedà, J. Llibre and R. Serra, Mimimal periodic orbits for continuous maps of the interval, Trans. Amer. Math. Soc. 286 (1984), 595-627.
  • [B] S. Baldwin, Generalizations of a theorem of Sharkovskii on orbits of continuous real-valued functions, Discrete Math. 67 (1987), 111-127.
  • [B1] L. Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391-398.
  • [B2] L. Block, Periodic orbits of continuous mappings of the circle, ibid. 260 (1980), 553-562.
  • [BGMY] L. Block, J. Guckenheimer, M. Misiurewicz and L. S. Young, Periodic points and topological entropy of one dimensional maps, in: Global Theory of Dynamical Systems, Lecture Notes in Math. 819, Springer, Berlin, 1980, 18-34.
  • [Bl] A. Blokh, Rotation numbers, twists and a Sharkovskii-Misiurewicz-type ordering for patterns on the interval, Ergodic Theory Dynam. Systems 15 (1995), 1331-1337.
  • [BM] A. Blokh and M. Misiurewicz, Entropy of twist interval maps, MSRI Preprint No. 041-94, Math. Sci. Res. Inst., Berkeley, 1994.
  • [BK] J. Bobok and M. Kuchta, Invariant measures for maps of the interval that do not have points of some period, Ergodic Theory Dynam. Systems 14 (1994), 9-21.
  • [C] W. A. Coppel, Šarkovskii-minimal orbits, Math. Proc. Cambridge Philos. Soc. 93 (1983), 397-408.
  • [HW] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, Oxford, 1960.
  • [LMPY] T.-Y. Li, M. Misiurewicz, G. Pianigiani and J. A. Yorke, No division implies chaos, Trans. Amer. Math. Soc. 273 (1982), 191-199.
  • [S] A. N. Sharkovskiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. Zh. 16 (1964), 61-71 (in Russian).
  • [St] P. Štefan, A theorem of Šarkovskiĭ on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), 237-248.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv156i1p33bwm
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