This article is cited in 1 paper

Special Issue: 70 Years of KAM Theory (Issue Editors: Alessandra Celletti, Luigi Chierchia, and Dmitry Treschev)

Isolated Diophantine Numbers

Fernando Argentieri^a, Luigi Chierchia<sup>b

a</sup> Institute of Mathematics, Zürich University, Winterthurerstrasse 190, 8057 Zürich, Switzerland
^b Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy

Abstract: In this note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with the same Diophantine constants), showing that Diophantine sets are not always Cantor sets.
General properties of isolated Diophantine numbers are also briefly discussed.

Keywords: Diophantine sets, Diophantine conditions, Cantor sets, KAM theory, small divisor problems

MSC: 37J40, 70H08, 11D75

Received: 30.11.2023
Accepted: 24.05.2024

Language: English

DOI: 10.1134/S156035472455001X