title: On the Liouville phenomenon in estimates of fractal dimensions of forced quasi-periodic oscillations
metadata.name: dc.contributor.author
metadata.value: Anikushin, Mikhail M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T15:09:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T15:09:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Anikushin M.M. On the Liouville Phenomenon in Estimates of Fractal Dimensions of Forced Quasi-Periodic Oscillations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 363–375.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16313
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We develop a method for studying fractal dimensions of forced almost periodic oscillations in various differential equations. The method is based on the previously introduced notion of the Diophantine dimension of an almost periodic function that is strictly connected with Diophantine approximations of its frequencies. Some estimates of the Diophantine dimension for typical quasi-periodic perturbations are obtained. For a class of control systems we state frequency-domain conditions under which the presented approach can be applied. As a result of our investigations one may observe a number-theoretic phenomenon (the Liouville phenomenon) arising within the mentioned problem. Its effect is in that we can not control fractal dimensions of quasi-periodic oscillations having well-approximable frequencies.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by the German-Russian Interdisciplinary Science Center (G-RISC) funded by the German Federal Foreign Office via the German Academic Exchange Service (DAAD) (project M-2017a-5, Project M-2017b-9) and the Leading Scientific Schools of Russia (project NSh-2858.2018.1).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: quasi-periodic function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dimension theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: diophantine approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: fractal dimension
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the Liouville phenomenon in estimates of fractal dimensions of forced quasi-periodic oscillations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 363-375.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16313/1/363-375.pdf
resources.format: Adobe PDF
resources.size: 361,61 kB