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Showing 1 to 4 of 4 for “"Arithmetic Dynamics"”.
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Effective integrality results in arithmetic dynamics
Given a rational function f defined over a number field K, S. Ih conjectured the finiteness of f-preperiodic points which are S-integral relative to a given non-preperiodic point β. This conjecture remains open, but certain special cases have been proved. We formulate a generalisation of Ih's …
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Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields
… arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial [mathematical expression], and an element [mathematical expression], the full …
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Some Connections Between Complex Dynamics and Statistical Mechanics
… The main techniques used come from holomorphic dynamics and more specifically the theories of activity/bifurcation currents and arithmetic dynamics. We prove a new equidistribution theorem that can be used to relate the chromatic zeros of a hierarchical lattice to the activity current of a …
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The Z-densities of the Fibonacci Sequence
Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is …