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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 314, Pages 272–284 (Mi znsl761)  
This article is cited in 11 scientific papers (total in 11 papers)

Derivatives of circle rotations and similarity of orbits

A. V. Shutov

Vladimir State Pedagogical University
Full-text PDF (185 kB) Citations (11)
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Abstract: It is proved that the derivative of a circle rotation on an arbitrary interval is either a circle rotation or a noncyclic exchange of three intervals. In the former case, all possible values of the new angle of rotation are computed. It is shown that the restriction of the orbit of a circle rotation to an eigeninterval of differentiation is similar to the orbit of another circle rotation.
Received: 15.07.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 133, Issue 6, Pages 1765–1771
DOI: https://doi.org/10.1007/s10958-006-0088-8
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: A. V. Shutov, “Derivatives of circle rotations and similarity of orbits”, Analytical theory of numbers and theory of functions. Part 20, Zap. Nauchn. Sem. POMI, 314, POMI, St. Petersburg, 2004, 272–284; J. Math. Sci. (N. Y.), 133:6 (2006), 1765–1771
Citation in format AMSBIB
\Bibitem{Shu04}
\by A.~V.~Shutov
\paper Derivatives of circle rotations and similarity of orbits
\inbook Analytical theory of numbers and theory of functions. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 314
\pages 272--284
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl761}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2119746}
\zmath{https://zbmath.org/?q=an:1082.37040}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 133
\issue 6
\pages 1765--1771
\crossref{https://doi.org/10.1007/s10958-006-0088-8}
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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