# American Institute of Mathematical Sciences

November  2008, 21(4): 977-1013. doi: 10.3934/dcds.2008.21.977

## Degree growth of matrix inversion: Birational maps of symmetric, cyclic matrices

 1 Department of Mathematics, Indiana University, Bloomington, IN 47405, United States, United States

Received  June 2007 Revised  February 2008 Published  May 2008

We consider two (densely defined) involutions on the space of $q\times q$ matrices; $I(x_{ij})$ is the matrix inverse of $(x_{ij})$, and $J(x_{ij})$ is the matrix whose $ij$th entry is the reciprocal $x_{ij}^{-1}$. Let $K=I\circ J$. The set $\mathcal{SC}_q$ of symmetric, cyclic matrices is invariant under $K$. In this paper, we determine the degrees of the iterates $K^n=K\circ...\circ K$ restricted to $\mathcal{SC}_q$.
Citation: Eric Bedford, Kyounghee Kim. Degree growth of matrix inversion: Birational maps of symmetric, cyclic matrices. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 977-1013. doi: 10.3934/dcds.2008.21.977
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