title: Sharkovskii’s ordering and evaluations of the number of periodic trajectories of given period of a self-map of an interval
metadata.name: dc.contributor.author
metadata.value: Ivanov, Oleg A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T16:44:31Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T16:44:31Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov O.A. Sharkovskii’s ordering and evaluations of the number of periodic trajectories of given period of a self-map of an interval. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 422–429.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16318
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In 1964, A. N. Sharkovskii published an article in which he introduced a special ordering on the set of positive integers. His ordering has the property that if p⊳q and a continuous mapping of an interval into itself has a point of period p, then it has a point of period q. Since the least number with respect to this ordering is the number 3, it follows that if such a mapping has a point of period 3, then it has points of every period. The latter result was rediscovered in 1975 by Li and Yorke, who published it in their paper “Period three implies chaos”. Their work led to global recognition of Sharkovskii’s theorem, and since then a great number of papers related to the study of mappings of an interval have appeared. One area of research concerns estimates of the number of periodic trajectories a map satisfying the conditions of Sharkovskyii’s theorem must have. In 1985, Bau-Sen Du published a paper in which he gave the exact lower bound for the number of periodic trajectories of a given period. The present article provides a new, significantly shorter and more natural proof of his result.
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: Sharkovsky’s ordering
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mappings of an interval
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: a periodical trajectory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: paths on directed graphs
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Sharkovskii’s ordering and evaluations of the number of periodic trajectories of given period of a self-map of an interval
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 422-429.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16318/1/422-429.pdf
resources.format: Adobe PDF
resources.size: 329,79 kB