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Sbornik: Mathematics, 2002, Volume 193, Issue 8, Pages 1203–1242
DOI: https://doi.org/10.1070/SM2002v193n08ABEH000676 (Mi sm676) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Topological and metric properties of a one-dimensional dynamical system in laser physics

G. S. Chakvetadze

Moscow Aviation Institute
English version PDF (422 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM2002v193n08ABEH000676
Abstract: The iterates of the real rational function $s_{a,b}(x)=b-ax/(1+x^2)$ are studied in their dependence on the parameters $a,b\in\mathbb R$. The parameter ranges corresponding to regular and chaotic dynamical behaviour of the system are determined. In particular, an analogue of Jakobson's theorem is proved for a two-parameter family of one-dimensional maps close to a certain map with a neutral fixed point.
Received: 01.11.2001
Bibliographic databases:
UDC: 517.987.5
MSC: Primary 37E05; Secondary 37A05
Language: English
Original paper language: Russian
Citation: G. S. Chakvetadze, “Topological and metric properties of a one-dimensional dynamical system in laser physics”, Sb. Math., 193:8 (2002), 1203–1242
Citation in format AMSBIB
\Bibitem{Cha02}
\by G.~S.~Chakvetadze
\paper Topological and metric properties of a one-dimensional dynamical system
in laser physics
\jour Sb. Math.
\yr 2002
\vol 193
\issue 8
\pages 1203--1242
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\zmath{https://zbmath.org/?q=an:1036.37032}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036662032}
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  • https://doi.org/10.1070/SM2002v193n08ABEH000676
  • https://www.mathnet.ru/eng/sm/v193/i8/p101
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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