Work

k-divergent lattices

Year: 2024

Type: article

Abstract: We introduce a novel concept in topological dynamics, referred to as $k$-divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogeneous Diophantine approximations, we investigate this notion in the dynamical system given by a certain flow on the space of unimodular lattices in $\mathbb{R}^d$. Our main result is the existence of $k$-divergent lattices for any $k\geq 0$. In fact, we utilize the emerging theory of parametric geometry of numbers and calculate the Hausdorff dimension of the set of $k$-divergent lattices.

Source: Combinatorics and Number Theory

DOI: 10.2140/cnt.2024.13.207

Authors: Guy Lachman, Anurag Rao, Uri Shapira, Yuval Yifrach

Institutions: Tel Aviv University, Peking University, Technion – Israel Institute of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

Award: G434337789