Dynamically distinguishing polynomials

  title={Dynamically distinguishing polynomials},
  author={Andrew Bridy and Derek Garton},
  journal={Research in the Mathematical Sciences},
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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  • J. Gathen
  • Computer Science, Mathematics
    Math. Comput.
  • 2019
A common measure of randomness, the entropy, is applied in the context of iterated functions on a finite set with n elements and turns out to be asymptotically close to log2 n minus the entropy of the vector of its cycle lengths.

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Corrigendum: ‘On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350’

  • P. Morton
  • Mathematics
    Compositio Mathematica
  • 2010
Abstract An argument is given to fill a gap in a proof in the author’s article On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350, that the polynomial

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