Minor cycles for interval maps

Michał Misiurewicz

Fundamenta Mathematicae (1994)

  • Volume: 145, Issue: 3, page 281-304
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Misiurewicz, Michał. "Minor cycles for interval maps." Fundamenta Mathematicae 145.3 (1994): 281-304. <http://eudml.org/doc/212047>.

@article{Misiurewicz1994,
abstract = {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.},
author = {Misiurewicz, Michał},
journal = {Fundamenta Mathematicae},
keywords = {interval maps; periodic orbit; -covering; Markov graph; Štefan cycle; entropy},
language = {eng},
number = {3},
pages = {281-304},
title = {Minor cycles for interval maps},
url = {http://eudml.org/doc/212047},
volume = {145},
year = {1994},
}

TY - JOUR
AU - Misiurewicz, Michał
TI - Minor cycles for interval maps
JO - Fundamenta Mathematicae
PY - 1994
VL - 145
IS - 3
SP - 281
EP - 304
AB - 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.
LA - eng
KW - interval maps; periodic orbit; -covering; Markov graph; Štefan cycle; entropy
UR - http://eudml.org/doc/212047
ER -

References

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  1. [ALMY] Ll. Alsedà, J. Llibre and M. Misiurewicz, Periodic orbits of maps of Y, Trans. Amer. Math. Soc. 313 (1989), 475-538 Zbl0803.54032
  2. [ALM] Ll. Alsedà, J. Llibre and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. Nonlinear Dynam. 5, World Scientific, 1993. Zbl0843.58034
  3. [BCMM] C. Bernhardt, E. Coven, M. Misiurewicz and I. Mulvey, Comparing periodic orbits of maps of the interval, Trans. Amer. Math. Soc., to appear. 
  4. [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. 
  5. [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 Zbl0793.58029
  6. [LMPY] T.-Y. Li, M. Misiurewicz, G. Pianigiani and J. Yorke, No division implies chaos, Trans. Amer. Math. Soc. 273 (1982), 191-199. Zbl0495.58018
  7. [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. Zbl0354.54027

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