69 research outputs found
On the Length of Critical Orbits of Stable Quadratic Polynomials
We use the Weil bound of multiplicative character sums together with some
recent results of N. Boston and R. Jones, to show that the critical orbit of
quadratic polynomials over a finite field of elements is of length
, improving upon the trivial bound
Pseudorandomness and Dynamics of Fermat Quotients
We obtain some theoretic and experimental results concerning various
properties (the number of fixed points, image distribution, cycle lengths) of
the dynamical system naturally associated with Fermat quotients acting on the
set . We also consider pseudorandom properties of Fermat
quotients such as joint distribution and linear complexity
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