On polynomial configurations in fractal sets

Kevin Henriot, Izabella Łaba, Malabika Pramanik

Type: Article

Publication Date: 2016-07-29

Citations: 23

DOI: https://doi.org/10.2140/apde.2016.9.1153

Abstract

We show that subsets of ‫ޒ‬ n of large enough Hausdorff and Fourier dimension contain polynomial patterns of the formwhere A i are real n × m matrices, Q is a real polynomial in m variables and e n = (0, . . ., 0, 1).

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