Minor cycles for interval maps

• Autorzy: Michał Misiurewicz
• Języki publikacji: EN

Abstrakty

EN

For continuous maps of an interval into itself we consider cycles (periodic orbits) that are non-reducible in the sense that there is no non-trivial partition into blocks of consecutive points permuted by the map. Among them we identify the miror ones. They are those whose existence does not imply existence of other non-reducible cycles of the same period. Moreover, we find minor patterns of a given period with minimal entropy.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 145
• Numer: 3
• Strony: 281-304

Daty

wydano

1994

otrzymano

1993-10-15

Twórcy

autor

Michał Misiurewicz

• Department of Mathematical Sciences, IUPUI 402 N. Blackford Street, Indianapolis, Indiana 46202-3216, U.S.A.

Bibliografia

• [ALMY] Ll. Alsedà, J. Llibre and M. Misiurewicz, Periodic orbits of maps of Y, Trans. Amer. Math. Soc. 313 (1989), 475-538
• [ALM] Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Scientific, 1993.
• [BCMM] C. Bernhardt, E. Coven, M. Misiurewicz and I. Mulvey, Comparing periodic orbits of maps of the interval, Trans. Amer. Math. Soc., to appear.
• [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.
• [FM] J. Franks and M. Misiurewicz, Cycles for disk homeomorphisms and thick trees, in: Nielsen Theory and Dynamical Systems, C. K. McCord (ed.), Contemp. Math. 152, Amer. Math. Soc., Providence, R.I., 1993, 69-139
• [LMPY] T.-Y. Li, M. Misiurewicz, G. Pianigiani and J. Yorke, No division implies chaos, Trans. Amer. Math. Soc. 273 (1982), 191-199.
• [S] P. Štefan, A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), 237-248.