Isolated Diophantine Numbers

2024, Volume 29, Number 4, pp. 536-540

Author(s): Argentieri F., Chierchia L.

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

Citation: Argentieri F., Chierchia L., Isolated Diophantine Numbers, Regular and Chaotic Dynamics, 2024, Volume 29, Number 4, pp. 536-540

DOI: 10.1134/S156035472455001X

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