On the transitive and ω -limit points of the continuous mappings of the circle

David Pokluda

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 1, page 49-52
  • ISSN: 0044-8753

Abstract

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We extend the recent results from the class 𝒞 ( I , I ) of continuous maps of the interval to the class 𝒞 ( 𝕊 , 𝕊 ) of continuous maps of the circle. Among others, we give a characterization of ω -limit sets and give a characterization of sets of transitive points for these maps.

How to cite

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Pokluda, David. "On the transitive and $\omega $-limit points of the continuous mappings of the circle." Archivum Mathematicum 038.1 (2002): 49-52. <http://eudml.org/doc/248934>.

@article{Pokluda2002,
abstract = {We extend the recent results from the class $\mathcal \{C\}(I,I)$ of continuous maps of the interval to the class $\mathcal \{C\}(\mathbb \{S\},\mathbb \{S\})$ of continuous maps of the circle. Among others, we give a characterization of $\omega $-limit sets and give a characterization of sets of transitive points for these maps.},
author = {Pokluda, David},
journal = {Archivum Mathematicum},
keywords = {dynamical system; circle map; -limit set; set of transitive points},
language = {eng},
number = {1},
pages = {49-52},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the transitive and $\omega $-limit points of the continuous mappings of the circle},
url = {http://eudml.org/doc/248934},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Pokluda, David
TI - On the transitive and $\omega $-limit points of the continuous mappings of the circle
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 49
EP - 52
AB - We extend the recent results from the class $\mathcal {C}(I,I)$ of continuous maps of the interval to the class $\mathcal {C}(\mathbb {S},\mathbb {S})$ of continuous maps of the circle. Among others, we give a characterization of $\omega $-limit sets and give a characterization of sets of transitive points for these maps.
LA - eng
KW - dynamical system; circle map; -limit set; set of transitive points
UR - http://eudml.org/doc/248934
ER -

References

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  1. Agronsky S. J., Bruckner A. M., Ceder J. G., Pearson T. L., The structure of ω -limit sets for continuous functions, Real Anal. Exchange 15 (1989/1990), 483–510. (1989) MR1059418
  2. Alsedà L., Llibre J., Misiurewicz M., Combinatorial Dynamics and Entropy in Dimension One, World Scientific Publ., Singapore 1993. (1993) MR1255515
  3. Block L. S., Coppel W. A., Dynamics in One Dimension, Lecture Notes in Math., vol. 1513, Springer, Berlin, 1992. (1992) Zbl0746.58007MR1176513
  4. Blokh A. M., On transitive mappings of one-dimensional ramified manifolds, in Differential-difference equations and problems of mathematical physics, Inst. Mat. Acad. Sci., Kiev, 1984, 3–9 (Russian). (1984) Zbl0605.58007MR0884346
  5. Kolyada S., Snoha, L’., Some aspects of topological transitivity – a survey, Iteration Theory (ECIT 94), Grazer Math. Ber. 334 (1997), 3–37. (1997) Zbl0907.54036MR1644768
  6. Pokluda D., Smítal J., A “universal” dynamical system generated by a continuous map of the interval, Proc. Amer. Math. Soc. 128 (2000), 3047–3056. Zbl0973.37025MR1712885
  7. Pokluda D., On the structure of sets of transitive points for continuous maps of the interval, Real Anal. Exchange, 25 (1999/2000), 45–48. (1999) 

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