On the Certain Properties of Bruin-Troubetzkoy Family of Interval Translation Mappings

Student: Kirill Zernikov

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2024

In this work we present general overview of the results related to interval translation mappings and their subclasses: double rotations and Bruin-Troubetzkoy family. We also give definition of Bruin-Troubetzkoy gasket and an elementary proof that its Hausdorff dimension is strictly less than two. Later using the same methods we improve this upper bound estimate to 1.9, which is a new result.

Full text (added June 2, 2024)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses