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Abstract for Edward J. Barbeau, John Chew and Stephen Tanny,
 A Matrix Dynamics Approach to Golomb's Recursion


In an unpublished note Golomb proposed a family of ``strange''
recursions of metafibonacci type, parametrized by $k$. Previously
we showed that contrary to Golomb's conjecture, for each $k$
there are many increasing solutions, and an explicit construction 
for multiple solutions was displayed. By reformulating our solution
approach using matrix dynamics, we extend these results to a
characterization of the asymptotic behaviour of all solutions of the
Golomb recursion. This matrix dynamics perspective is also used to
construct what we believe is the first example of a ``nontrivial''
nonincreasing solution, that is, one that is not eventually
increasing.
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