Year: 2025
Type: preprint
Abstract: We prove that for any function $f$ satisfying certain mild conditions and any Cantor set $K$ with Newhouse thickness greater than $1$, there exists $x\in K$ and $t>0$ such that \[ \{x-t,x,x+f(t)\}\subset K. \] This is an extension of previous work on the existence of three-term arithmetic progressions in Cantor sets to the non-linear setting.
Source: arXiv (Cornell University)
Authors: McDonald, Alex, Nguyen, Micah
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416257361
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