On a Family of Circle Homeomohphisms with One Break Point

  • Karshiboev Khayrullo Kilichovich Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Higher Mathematics, Samarkand Institute of Economics and Service
DOI: https://doi.org/10.17605/ijie.v5i4.2975
Keywords: circle homeomorphism, renormalization, rotation number

Abstract

this article, we study a one-parameter family of circle homeomorphisms with one break point. It is proved that in the case of a rational rotation number the number of periodic trajectories does not exceed two.

References

1. K. M. Khanin and E. B. Vul. Circle Homeomorphisms with weak Discontinuities. Advances in Soviet Mathematics, v. 3, 1991, p. 57-98.
2. I.P. Kornfeld, Ya.G. Sinai, S.V. Fomin. Ergodictheory. –M. Science, 1980.
3. H.K. Karshiboev. Behavior of renormalizations of ergodic mappings of a circle with a break// Uzbek mathematical journal. - Tashkent, 2009. - No. 4. -p.82-95.
Published
2022-04-21
How to Cite
[1]
Kilichovich, K.K. 2022. On a Family of Circle Homeomohphisms with One Break Point. International Journal on Integrated Education. 5, 4 (Apr. 2022), 171-175. DOI:https://doi.org/10.17605/ijie.v5i4.2975.
Issue
Vol. 5 No. 4 (2022): IJIE
Section
Articles
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