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Regular and Chaotic Dynamics, 2024, Volume 29, Issue 4, Pages 536–540
DOI: https://doi.org/10.1134/S156035472455001X (Mi rcd1268) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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

Isolated Diophantine Numbers

Fernando Argentieria, Luigi Chierchiab

a 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
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DOI: https://doi.org/10.1134/S156035472455001X
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
Funding agency
Research partially supported by the grant NRR-M4C2-I1.1-PRIN 2022-PE1-Stability in Hamiltonian dynamics and beyond-F53D23002730006-Financed by E.U.–NextGenerationEU.
Received: 30.11.2023
Accepted: 24.05.2024
Document Type: Article
MSC: 37J40, 70H08, 11D75
Language: English
Citation: Fernando Argentieri, Luigi Chierchia, “Isolated Diophantine Numbers”, Regul. Chaotic Dyn., 29:4 (2024), 536–540
Citation in format AMSBIB
\Bibitem{ArgChi24}
\by Fernando Argentieri, Luigi Chierchia
\paper Isolated Diophantine Numbers
\jour Regul. Chaotic Dyn.
\yr 2024
\vol 29
\issue 4
\pages 536--540
\mathnet{http://mi.mathnet.ru/rcd1268}
\crossref{https://doi.org/10.1134/S156035472455001X}
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