Alina Ostafe
Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems.
Втр, 09/06/2011 - 15:01 — SomNambulAuthors: Alina Ostafe, Igor Shparlinski
Subjects: Number Theory
AbstractWe introduce and study algebraic dynamical systems generated by triangular
systems of rational functions. We obtain several results about the degree
growth and linear independence of iterates as well as about possible lengths of
trajectories generated by such dynamical systems over finite fields. Some of
these results are generalisations of those known in the polynomial case, some
are new even in this case.Pseudorandomness and Dynamics of Fermat Quotients.
Втр, 01/12/2010 - 16:01 — SomNambulAuthors: Alina Ostafe, Igor Shparlinski
Subjects: Number Theory
AbstractWe 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 $\{0, ..., p-1\}$. We also consider pseudorandom properties of Fermat
quotients such as joint distribution and linear complexity.On the Length of Critical Orbits of Stable Quadratic Polynomials.
Ср, 09/23/2009 - 13:19 — SomNambulAuthors: Igor E. Shparlinski, Alina Ostafe
Subjects: Number Theory
AbstractWe use bounds 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 $q$ elements is of length $O(q^{3/4})$,
improving upon the trivial bound $q$.On the Length of Critical Orbits of Stable Quadratic Polynomials.
Ср, 09/23/2009 - 13:19 — SomNambulAuthors: Igor E. Shparlinski, Alina Ostafe
Subjects: Number Theory
AbstractWe use bounds 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 $q$ elements is of length $O(q^{3/4})$,
improving upon the trivial bound $q$.Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials.
Втр, 09/01/2009 - 12:47 — SomNambulAuthors: Igor E. Shparlinski, Alina Ostafe
Subjects: Number Theory
AbstractDynamical systems generated by iterations of multivariate polynomials with
slow degree growth have proved to admit good estimates of exponential sums
along their orbits which in turn lead to rather stronger bounds on the
discrepancy for pseudorandom vectors generated by these iterations. Here we add
new arguments to our original approach and also extend some of our recent
constructions and results to more general orbits of polynomial iterations which
may involve distinct polynomials as well.- Читать далее
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