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2016 On polynomial configurations in fractal sets
Kevin Henriot, Izabella Łaba, Malabika Pramanik
Anal. PDE 9(5): 1153-1184 (2016). DOI: 10.2140/apde.2016.9.1153

Abstract

We show that subsets of n of large enough Hausdorff and Fourier dimension contain polynomial patterns of the form

(x,x + A1y,,x + Ak1y,x + Aky + Q(y)en),x n,y m,

where Ai are real n × m matrices, Q is a real polynomial in m variables and en = (0,,0,1).

Citation

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Kevin Henriot. Izabella Łaba. Malabika Pramanik. "On polynomial configurations in fractal sets." Anal. PDE 9 (5) 1153 - 1184, 2016. https://doi.org/10.2140/apde.2016.9.1153

Information

Received: 25 November 2015; Revised: 29 March 2016; Accepted: 29 April 2016; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 06608422
MathSciNet: MR3531369
Digital Object Identifier: 10.2140/apde.2016.9.1153

Subjects:
Primary: 11B30
Secondary: 28A80

Rights: Copyright © 2016 Mathematical Sciences Publishers

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