Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskie Zametki, 2023, Volume 114, Issue 2, Pages 229–243
DOI: https://doi.org/10.4213/mzm13612
(Mi mzm13612)
 

This article is cited in 1 scientific paper (total in 1 paper)

Perturbations of Nonhyperbolic Algebraic Automorphisms of the 2-Torus

V. Z. Grines, D. I. Mints, E. E. Chilina

National Research University – Higher School of Economics in Nizhny Novgorod
Full-text PDF (814 kB) Citations (1)
References:
Abstract: All nonhyperbolic automorphisms of the 2-torus are not structurally stable, and it is generally impossible to predict the dynamics of their arbitrarily small perturbations. In this paper, given a representative of each algebraic conjugacy class of nonperiodic nonhyperbolic maps, a one-parameter family of diffeomorphisms is constructed, in which the zero value of the parameter corresponds to the given map and the nonzero values, to Morse–Smale diffeomorphisms. According to results of V. Z. Grines and A. N. Bezdenezhnykh, a Morse–Smale diffeomorphism of a closed orientable surface which induces a nonperiodic action on the fundamental group has nonempty heteroclinic set. It is proved that, in all of the constructed families, the diffeomorphisms corresponding to nonzero parameter values have nonempty orientable heteroclinic sets in which the number of orbits is determined by the automorphism being perturbed.
Keywords: nonhyperbolic automorphism, $2$-torus, orientable heteroclinic set.
Funding agency Grant number
HSE Academic Fund Programme 21-04-004
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1101
The publication was prepared within the framework of the Academic Fund Program at the HSE University in 2021–2022 (grant no. 21-04-004), except for the work on Sec. 2, which was supported by the Laboratory of Dynamical Systems and Applications NRU HSE, grant of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-1101).
Received: 05.06.2022
Revised: 15.11.2022
English version:
Mathematical Notes, 2023, Volume 114, Issue 2, Pages 187–198
DOI: https://doi.org/10.1134/S0001434623070209
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 37C05
Language: Russian
Citation: V. Z. Grines, D. I. Mints, E. E. Chilina, “Perturbations of Nonhyperbolic Algebraic Automorphisms of the 2-Torus”, Mat. Zametki, 114:2 (2023), 229–243; Math. Notes, 114:2 (2023), 187–198
Citation in format AMSBIB
\Bibitem{GriMinChi23}
\by V.~Z.~Grines, D.~I.~Mints, E.~E.~Chilina
\paper Perturbations of Nonhyperbolic Algebraic Automorphisms of the 2-Torus
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 2
\pages 229--243
\mathnet{http://mi.mathnet.ru/mzm13612}
\crossref{https://doi.org/10.4213/mzm13612}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4634786}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 2
\pages 187--198
\crossref{https://doi.org/10.1134/S0001434623070209}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85168568676}
Linking options:
  • https://www.mathnet.ru/eng/mzm13612
  • https://doi.org/10.4213/mzm13612
  • https://www.mathnet.ru/eng/mzm/v114/i2/p229
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:193
    Full-text PDF :32
    Russian version HTML:146
    References:32
    First page:11
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024