Mathematics – Dynamical Systems
Scientific paper
2011-04-29
Mathematics
Dynamical Systems
Scientific paper
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ $(w=(w_n), n\in \nit)$ consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.}
Belov Ya. A.
Kondakov G. V.
Mitrofanov Igor
No associations
LandOfFree
Inverse problems of symbolic dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Inverse problems of symbolic dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inverse problems of symbolic dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-17522