title: On the density of pre-orbits under linear toral endomorphisms
metadata.name: dc.contributor.author
metadata.value: Azimi, Saeed
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tajbakhsh, Khosro
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-09-10T13:12:08Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T13:12:08Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Azimi S., Tajbakhsh Kh. On the density of pre-orbits under linear toral endomorphisms. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 369–376.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19388
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: It is well known for non-injective endomorphisms that if for every point the set of preimages
  is dense in the manifold then the endomorphism is transitive (i. e. there exists a point that
  its orbit is dense in the manifold). But it has not yet been completely investigated that if
  the pre-orbit of points are dense under Anosov endomorphisms or what are the necessary
  conditions that make the pre-orbits of each point dense. By making a great use of the
  integral lattice properties, we construct our proof on the pre-image sets of points under
  the iterations of the linear dynamical system. We introduce a class of hyperbolic linear
  endomorphism that is called absolutely hyperbolic and show that if A : Tm → T
  m is an
  absolutely hyperbolic linear endomorphism of degree more than 1 then the pre-orbit of each
  point is dense in Tm.
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 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: linear endomorphism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: hyperbolicity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: transitivity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: dynamical systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Anosov maps
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the density of pre-orbits under linear toral endomorphisms
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 369-376.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19388/1/369-376.pdf
resources.format: Adobe PDF
resources.size: 290,95 kB