Loading [MathJax]/jax/output/SVG/config.js
Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find




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

Zapiski Nauchnykh Seminarov POMI, 2015, Volume 432, Pages 261–273 (Mi znsl6120)  
This article is cited in 2 scientific papers (total in 2 papers)

Shadowing in linear skew products

S. Tikhomirovab

a Chebyshev Laboratory, St. Petersburg State Univeristy, 14th line of Vasilievsky Island, 29B, St. Petersburg 199178, Russia
b Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig, 04103, Germany
Full-text PDF (200 kB) Citations (2)
References:
PDF
HTML
Abstract: We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result indicates that the high-dimensional analog of the Hammel–Yorke–Grebogi conjecture concerning the interval of shadowability for a typical pseudotrajectory is not correct. The main technique is the reduction of the shadowing problem to the ruin problem for a simple random walk.
Key words and phrases: shadowing, skew product, random walk, large deviation principle.
Received: 03.11.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 6, Pages 979–987
DOI: https://doi.org/10.1007/s10958-015-2541-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: S. Tikhomirov, “Shadowing in linear skew products”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 261–273; J. Math. Sci. (N. Y.), 209:6 (2015), 979–987
Citation in format AMSBIB
\Bibitem{Tik15}
\by S.~Tikhomirov
\paper Shadowing in linear skew products
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 261--273
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6120}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 979--987
\crossref{https://doi.org/10.1007/s10958-015-2541-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939459016}
Linking options:
  • https://www.mathnet.ru/eng/znsl6120
  • https://www.mathnet.ru/eng/znsl/v432/p261
    • This publication is cited in the following 2 articles:
    1. P. A. Priezzhev, V. A. Priezzhev, S. B. Tikhomirov, “Probabilistic Shadowing for Pseudotrajectories with Decreasing Errors”, J Math Sci, 281:1 (2024), 142  crossref
    2. V. A. Priezzhev, P. A. Priezzhev, S. B. Tikhomirov, “Veroyatnostnoe otslezhivanie dlya psevdotraektorii s ubyvayuschimi oshibkami”, Veroyatnost i statistika. 31, Zap. nauchn. sem. POMI, 505, POMI, SPb., 2021, 207–229  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:290
    Full-text PDF :69
    References:60
     
      Contact us:
    math-net2025_04@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025