Finite Point configurations in Products of Thick Cantor sets and a
Robust Nonlinear Newhouse Gap Lemma
Finite Point configurations in Products of Thick Cantor sets and a
Robust Nonlinear Newhouse Gap Lemma
In this paper we prove that the set of tuples of edge lengths in $K_1\times K_2$ corresponding to a finite tree has non-empty interior, where $K_1,K_2\subset \mathbb{R}$ are Cantor sets of thickness $\tau(K_1)\cdot \tau(K_2) >1$. Our method relies on establishing that the pinned distance set is robust to small perturbations …