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

Details Degree growth of matrix inversion: birational maps of symmetric, cyclic matrices Degree growth of matrix inversion: birational maps of symmetric, cyclic matrices

2005-12-21

arxiv.org/abs/math/0512507v1

Mathematics

Dynamical Systems

Scientific paper

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 ${\cal SC}_q$ 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 ${\cal SC}_q$.

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