# 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…

## 6 Citations

### The Cycle Structure of Unicritical Polynomials

- MathematicsInternational Mathematics Research Notices
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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 $…

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. Fix an odd prime p . If r is a positive integer and f a polynomial with coef-ﬁcients in F p r , let P p,r ( f ) be the proportion of P 1 ( F p r ) that is periodic with respect to f . We show that…

### A Galois–Dynamics Correspondence for Unicritical Polynomials

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In an analogy with the Galois homothety property for torsion points of abelian varieties that was used in the proof of the Mordell–Lang conjecture, we describe a correspondence between the action of…

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This work introduces efficient algorithms for methodical computations and provides the values of various direct and cumulative statistical parameters of interest, particularly on connected functional graphs generated by quadratic polynomials over prime fields.

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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.

### Bayesian analysis of the inverse generalized gamma distribution using objective priors

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The inverse generalized gamma (IGG) distribution can be particularly useful for modelling reliability (survival) data with an upside-down bathtub hazard rate function. The mathematical properties and…

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