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Sbornik: Mathematics, 2002, Volume 193, Issue 8, Pages 1203–1242
DOI: https://doi.org/10.1070/SM2002v193n08ABEH000676 (Mi sm676) 		 
Topological and metric properties of a one-dimensional dynamical system in laser physics

G. S. Chakvetadze

Moscow Aviation Institute
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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
Russian version:
Matematicheskii Sbornik, 2002, Volume 193, Number 8, Pages 101–140
DOI: https://doi.org/10.4213/sm676
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”, Mat. Sb., 193:8 (2002), 101–140; Sb. Math., 193:8 (2002), 1203–1242
Citation in format AMSBIB
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    English version PDF:9
    References:53
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