Dynamically distinguishing polynomials

@article{Bridy2016DynamicallyDP,
  title={Dynamically distinguishing polynomials},
  author={Andrew Bridy and Derek Garton},
  journal={Research in the Mathematical Sciences},
  year={2016},
  volume={4},
  pages={1-17}
}
A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field $${\mathbb {F}}_p$$Fp. We say a subset of $${\mathbb {Z}}[x]$$Z[x] is dynamically distinguishable mod p if the associated mod p dynamical systems are pairwise non-isomorphic. For any $$k,M\in {\mathbb {Z}}_{>1}$$k,M∈Z>1, we prove that there are infinitely many sets of integers $${\mathcal {M}}$$M of size M… 

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