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{\bf Jason P. Bell, Stanley N. Burris and Karen A. Yeats}
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{\bf Characteristic Points of Recursive Systems }
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Characteristic points have been a primary tool in the study of a
generating function defined by a single recursive equation.  We
investigate the proper way to adapt this tool when working with
multi-equation recursive systems.
						
Given an irreducible non-negative power series system with $m$
equations, let $\rho$ be the radius of convergence of the solution
power series and let $\pmb{\tau}$ be the values of the solution series
evaluated at $\rho$.  The main results of the paper include:
\begin{enumerate}
\item[(a)] the set of characteristic points form an antichain in
  ${\mathbb R}^{m+1}$,
\item[(b)] given a characteristic point $(a,\mathbf{b})$, (i) the spectral
  radius of the Jacobian of $\pmb \gamma$ at $(a, \mathbf{b})$ is $\ge 1$, and
  (ii) it is $=1$ iff $(a,\mathbf{b}) = (\rho,\pmb{\tau})$,
\item[(c)] if $(\rho,\pmb{\tau})$ is a characteristic point, then (i)
  $\rho$ is the largest $a$ for $(a,\mathbf{b})$ a characteristic
  point, and (ii) a characteristic point $(a,\mathbf{b})$ with
  $a=\rho$ is the extreme point $(\rho,\pmb{\tau})$.
\end{enumerate}

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