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Fundamentalnaya i Prikladnaya Matematika, 2005, Volume 11, Issue 5, Pages 47–55 (Mi fpm862)  

This article is cited in 1 scientific paper (total in 1 paper)

A bound for the topological entropy of homeomorphisms of a punctured two-dimensional disk

O. N. Biryukov

Kolomna State Pedagogical Institute
Full-text PDF (140 kB) Citations (1)
References:
Abstract: We consider homeomorphisms $f$ of a punctured 2-disk $D^2\setminus P$, where $P$ is a finite set of interior points of $D^2$, which leave the boundary points fixed. Any such homeomorphism induces an automorphism $f_*$ of the fundamental group of $D^2\setminus P$. Moreover, to each homeomorphism $f$, a matrix $B_f(t)$ from $\mathrm{GL}(n,\mathbb Z[t,t^{-1}])$ can be assigned by using the well-known Burau representation. The purpose of this paper is to find a nontrivial lower bound for the topological entropy of $f$. First, we consider the lower bound for the entropy found by R. Bowen by using the growth rate of the induced automorphism $f_*$. Then we analyze the argument of B. Kolev, who obtained a lower bound for the topological entropy by using the spectral radius of the matrix $B_f(t)$, where $t\in\mathbb C$, and slightly improve his result.
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 146, Issue 1, Pages 5483–5489
DOI: https://doi.org/10.1007/s10958-007-0360-6
Bibliographic databases:
UDC: 515.162.8+517.938.5+515.122.4
Language: Russian
Citation: O. N. Biryukov, “A bound for the topological entropy of homeomorphisms of a punctured two-dimensional disk”, Fundam. Prikl. Mat., 11:5 (2005), 47–55; J. Math. Sci., 146:1 (2007), 5483–5489
Citation in format AMSBIB
\Bibitem{Bir05}
\by O.~N.~Biryukov
\paper A bound for the topological entropy of homeomorphisms of a~punctured two-dimensional disk
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 5
\pages 47--55
\mathnet{http://mi.mathnet.ru/fpm862}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2216851}
\zmath{https://zbmath.org/?q=an:1149.37311}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 146
\issue 1
\pages 5483--5489
\crossref{https://doi.org/10.1007/s10958-007-0360-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548781987}
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  • https://www.mathnet.ru/eng/fpm862
  • https://www.mathnet.ru/eng/fpm/v11/i5/p47
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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    Abstract page:306
    Full-text PDF :130
    References:46
     
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