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- W2108359623 abstract "We consider iterations of integer-valued functions $phi$, which have no fixed points in the domain of positive integers. We define a local function $phi_n$, which is a sub-function of $phi$ being restricted to the subdomain ${0, ..., n }$. The iterations of $phi_n$ can be described by a certain $n times n$ sparse matrix $M_n$ and its powers. The determinant of the related $n times n$ matrix $hat{M}_n = I - M_n$, where $I$ is the identity matrix, acts as an indicator, whether the iterations of the local function $phi_n$ enter a cycle or not. If $phi_n$ has no cycle, then $det hat{M}_n = 1$ and the structure of the inverse $hat{M}_n^{-1}$ can be characterized. Subsequently, we give applications to compute the inverse $hat{M}_n^{-1}$ for some special functions. At the end, we discuss the results in connection with the $3x+1$ and related problems." @default.
- W2108359623 created "2016-06-24" @default.
- W2108359623 creator A5040106908 @default.
- W2108359623 date "2014-11-03" @default.
- W2108359623 modified "2023-09-27" @default.
- W2108359623 title "Sparse matrices describing iterations of integer-valued functions" @default.
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- W2108359623 hasPublicationYear "2014" @default.
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