CIRCLE MAPPINGS WITH BREAKS

Authors

  • Khayrullo Kilichovich Karshiboev Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Higher Mathematics, Samarkand Institute of Economics and Service, Republic of Uzbekistan, Samarkand

Keywords:

circle homeomorphism, renormalization, rotation number.

Abstract

In 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

Джалилов А.А., Каршибоев Х.К. Предельные теоремы для времени попаданий отображений окружности с одной точкой излома. // Успехи математических наук. – Москва: 2004.- т. 59. вып. 1(355), с. 185-186.

Khanin K.M. and Vul E.V. Circle Homeomorphisms with weak Discontinuities. Advances in Soviet Mathematics, v. 3, 1991, p. 57-98.

Корнфельд И.П., Синай Я.Г., Фомин С.В. Эргодическая теория. –М.: Наука, 1980.

Синай Я.Г. Современные проблемы эргодической теории. - М.: Наука, 1995.

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Published

2023-04-16

How to Cite

Karshiboev , K. K. (2023). CIRCLE MAPPINGS WITH BREAKS. Innovative Development in Educational Activities, 2(7), 376–381. Retrieved from https://openidea.uz/index.php/idea/article/view/1045

Issue

Vol. 2 No. 7 (2023): Innovative Development in Educational Activities (IDEA)

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.