title: An estimate for the number of periodical trajectories of the given period for a mapping of an interval, Lucas numbers, and necklaces
metadata.name: dc.contributor.author
metadata.value: Ivanov, Oleg А.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:30:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:30:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanov O. A. An estimate for the number of periodical trajectories of the given period for a mapping of an interval, Lucas numbers, and necklaces. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 606–613.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.406
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15128
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In 1964, A. N. Sharkovsky published an article in which he introduced a special ordering
  on the set of positive integers. This ordering has the property that if p   q and a mapping
  of an interval into itself has a point of period p, then it has a point of period q. The least
  number with respect to this ordering is the number 3. Thus, if a mapping has a point
  of period 3, then this mapping has points of any periods. In 1975, the latter result was
  rediscovered by Li and Yorke, who published the paper “Period three implies chaos”. In
  that paper, an exact lower bound for the number of trajectories of a given period for a
  mapping of an interval into itself, which has a point of period 3 is given. The key point
  of the reasoning consisted in solution of one combinatorial problem, the answer to which
  is expressed in terms of the Lucas numbers. As a consequence, an explicit formula for the
  number of necklaces of a special type is obtained. The article also examined a particular
  piecewise linear unimodular mapping of an interval [0, 1] into itself for which it is possible
  to find points of an arbitrary given period.
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 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: periodical trajectory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mappings of an interval
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Sharkovsky’s ordering
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lucas numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: number of necklaces
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: An estimate for the number of periodical trajectories of the given period for a mapping of an interval, Lucas numbers, and necklaces
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Ivanov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15128/1/06-Ivanov.pdf
resources.format: Adobe PDF
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