
Keldysh Institute preprints, 2002, 043
(Mi ipmp1017)




Lagrange spectrum and dynamics on the invariant sets of linearfractional IFSs
A. I. Aptekarev^{}, M. A. Lapik^{}
Abstract:
A geometrical approach to investigation of Lagrange spectrum over finite fields, i.e. for the real numbers whose continues fraction expansions contain coefficients from a fixed finite set of natural numbers, is proposed. The real number under investigation defines dynamics on the invariant sets of iterated functional system (IFS) of linearfractional transformations with the coefficients from this fixed set of natural numbers. The value of the point of Lagrange spectrum corresponding to the real number then can be expressed by means of some geometrical characteristic of this dynamics. Proposed approach is illustrated by demonstrations of known results on structure of Lagrange spectrum for the numbers whose continued fractions coefficients are 1 or 2 (i.e. left part of the spectrum).
Full text:
http:/.../preprint.asp?id=200243&lg=r
Citation:
A. I. Aptekarev, M. A. Lapik, “Lagrange spectrum and dynamics on the invariant sets of linearfractional IFSs”, Keldysh Institute preprints, 2002, 043
Citation in format AMSBIB
\Bibitem{AptLap02}
\by A.~I.~Aptekarev, M.~A.~Lapik
\paper Lagrange spectrum and dynamics on the invariant sets of linearfractional IFSs
\jour Keldysh Institute preprints
\yr 2002
\papernumber 043
\mathnet{http://mi.mathnet.ru/ipmp1017}
Linking options:
http://mi.mathnet.ru/eng/ipmp1017 http://mi.mathnet.ru/eng/ipmp/y2002/p43
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles

Number of views: 
This page:  126  Full text:  20 
