2 citations · 2 across the 2 of their papers we have counts for
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Linear Recurrences in the Degree Sequences of Monomial Mappings
Eric Bedford, Kyounghee Kim
Let be an integer matrix, and let be the associated monomial map. We give a connection between the eigenvalues of and existence of a linear recurrence relation in the…
The Number of Periodic Orbits of a Rational Difference Equation
Eric Bedford, Kyounghee Kim
We show how a variant of the Lefschetz Fixed Point Theorem may be used to count the number of periodic orbits for certain rational difference equations.
Periodicities in Linear Fractional Recurrences: Degree growth of birational surface maps
Eric Bedford, Kyounghee Kim
We consider the set of all 2-step recurrences (difference equations) that are given by linear fractional maps. These give birational maps of the plane. We determine the degree grow…
On the Degree Growth of Birational Mappings in Higher Dimension
Eric Bedford, Kyounghee Kim
Let be a birational map of , and consider the degree complexity, or asymptotic degree growth rate . We introduce a fami…