A genetic algorithm generates new extreme examples of small heights, many preperiodic points, long cycles, and long tails for polynomials up to degree 13 and rational functions up to degree 5.
The multiplier spectrum morphism is generically injective
2 Pith papers cite this work. Polarity classification is still indexing.
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For general rational functions A of degree m >= 2, decompositions of iterates A^n are unique up to equivalence, implying product maps on CP1 x CP1 have non-trivial periodic curves iff the component functions are conjugate.
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A Genetic Algorithm for Generating Extreme Examples in Arithmetic Dynamics
A genetic algorithm generates new extreme examples of small heights, many preperiodic points, long cycles, and long tails for polynomials up to degree 13 and rational functions up to degree 5.
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Periodic curves for general endomorphisms of $\mathbb C\mathbb P^1\times \mathbb C\mathbb P^1$
For general rational functions A of degree m >= 2, decompositions of iterates A^n are unique up to equivalence, implying product maps on CP1 x CP1 have non-trivial periodic curves iff the component functions are conjugate.