TL;DR
This paper investigates the properties of the left endpoints of the Lagrange spectrum and explores the concept of attainable numbers, contributing to the understanding of Diophantine approximation.
Contribution
It provides new insights into the structure of attainable numbers and the behavior of the Lagrange spectrum's left endpoints.
Findings
Characterization of attainable numbers
Properties of the Lagrange spectrum's left endpoints
New results on the structure of the spectrum
Abstract
The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.
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