A note on semi-regular continued fractions with bounded partial quotients
Kadyrov S. Kazin A. Duisen S.
2026Springer Science and Business Media Deutschland GmbH
Arabian Journal of Mathematics
2026
This paper explores Diophantine approximation and its connection to continued fractions. A number is called “badly approximable” if its regular continued fraction expansion has bounded partial quotients. These numbers have interesting geometric properties, such as full Hausdorff dimension but zero Lebesgue measure. We extend this idea to semi-regular continued fractions, a variation that uses a sequence of signs to modify the representation. We define σ-badly approximable numbers as those with bounded partial quotients in a semi-regular continued fractions for a fixed sequence of signs σ. This leads us to investigate the fractal properties of such numbers.
Text of the article Перейти на текст статьи
Department of General Education, New Uzbekistan University, Tashkent, Uzbekistan
Department of Mathematics and Natural Sciences, SDU University, Kaskelen, Kazakhstan
Department of General Education
Department of Mathematics and Natural Sciences
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026