Ergodic Averages for Independent Polynomials and Applications

Details Ergodic Averages for Independent Polynomials and Applications Ergodic Averages for Independent Polynomials and Applications

2004-12-08

arxiv.org/abs/math/0412177v2

Mathematics

Dynamical Systems

12 pages

Scientific paper

Szemer\'edi's Theorem states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman generalized this, showing that sets of integers with positive upper density contain arbitrarily long polynomial configurations; Szemer\'edi's Theorem corresponds to the linear case of the polynomial theorem. We focus on the case farthest from the linear case, that of rationally independent polynomials. We derive results in ergodic theory and in combinatorics for rationally independent polynomials, showing that their behavior differs sharply from the general situation.

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