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

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

Eric Bedford 1, and  Kyounghee Kim 1,

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 $\mathcal{SC}_q$.
Keywords: Birational maps., Degree growth.
Mathematics Subject Classification: Primary: 37F10; Secondary: 14J9.
Citation: Eric Bedford, Kyounghee Kim. Degree growth of matrix inversion: Birational maps of symmetric, cyclic matrices. Discrete & Continuous Dynamical Systems, 2008, 21 (4) : 977-1013. doi: 10.3934/dcds.2008.21.977
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