Buchumschlag

Evolution of the Sharkovsky theorem

UDC 517.9 We briefly describe some results that evolved from the Sharkovsky theorem.

Gespeichert in:
Bibliographische Detailangaben
Datum:2024
Hauptverfasser: Blokh, Alexander, Misiurewicz, Michał
Format: Artikel
Sprache:Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2024
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/7641
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
Завантажити файл: Pdf

Institution

Ukrains’kyi Matematychnyi Zhurnal
_version_ 1860512698656096256
author Blokh, Alexander
Misiurewicz, Michał
Blokh, Alexander
Misiurewicz, Michał
author_facet Blokh, Alexander
Misiurewicz, Michał
Blokh, Alexander
Misiurewicz, Michał
author_sort Blokh, Alexander
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2024-06-19T00:35:05Z
description UDC 517.9 We briefly describe some results that evolved from the Sharkovsky theorem.
doi_str_mv 10.3842/umzh.v76i1.7641
first_indexed 2026-03-24T03:32:55Z
format Article
fulltext Skip to main content Log in Menu Find a journal Publish with us Track your research Search Saved research Cart Home Ukrainian Mathematical Journal Article Evolution of the Sharkovsky Theorem Published: 30 July 2024 Volume 76, pages 51–64, (2024) Cite this article Save article View saved research Ukrainian Mathematical Journal Aims and scope Submit manuscript Alexander Blokh1 & Michał Misiurewicz2  45 Accesses Explore all metrics We briefly describe some results that evolved from the Sharkovsky theorem. This is a preview of subscription content, log in via an institution to check access. Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. Institutional subscriptions Similar content being viewed by others Application of the Randomized Sharkovsky-Type Theorems to Random Impulsive Differential Equations and Inclusions Article 09 July 2018 Selectivity Estimation for SPARQL Triple Patterns with Shape Expressions Chapter © 2018 Sharp Decay for Teukolsky Equation in Kerr Spacetimes Article Open access 08 February 2023 Explore related subjects Discover the latest articles, books and news in related subjects, suggested using machine learning. Differential Geometry History of Physics and Astronomy History of Science Mathematics Mathematical Physics Stellar evolution Invariant Manifolds and Dynamical Systems Analysis References Ll. Alsedà, D. Juher, and P. Mumbrú, “Periodic behavior on trees,” Ergodic Theory Dynam. Systems, 25, 1373–1400 (2005). Ll. Alsedà, J. Llibre, and M. Misiurewicz, “Periodic orbits of maps of Y,” Trans. Amer. Math. Soc., 313, 475–538 (1989). Ll. Alsedà, J. Llibre, and M. Misiurewicz, “Combinatorial dynamics and entropy in dimension one,” 2nd ed., Adv. Ser. Nonlin. Dynam., 5, World Scientific Publ. Co., Inc., River Edge, NJ (2000). Ll. Alsedà and M. Misiurewicz, “Linear orderings and the sets of periods for star maps,” J. Math. Anal. Appl., 285, 50–61 (2003). Ll. Alsedà and J. M. Moreno, “Linear orderings and the full periodicity kernel for the n-star,” J. Math. Anal. Appl., 180, 599–616 (1993). S. Baldwin, “An extension of Šarkovskiĭ’s theorem to the n-od,” Ergodic Theory Dynam. Syst., 11, 249–271 (1991). Article  Google Scholar  L. Block, J. Guckenheimer, M. Misiurewicz, and L.-S. Young, “Periodic points and topological entropy of one dimensional maps,” Lecture Notes Math., 819, Springer, Berlin (1980). L. Block, “Periods of periodic points of maps of the circle which have a fixed point,” Proc. Amer. Math. Soc., 82, 481–486 (1981). Article  MathSciNet  Google Scholar  A. Blokh, On Some Properties of Graph Maps: Spectral Decomposition, Misiurewicz Conjecture and Abstract Sets of Periods, Preprint #35, Max-Planck-Institut für Mathematik (1991). A. Blokh, “On rotation intervals for interval maps,” Nonlinearity, 7, 1395–1417 (1994). Article  MathSciNet  Google Scholar  A. Blokh, “Functional rotation numbers for one-dimensional maps,” Trans. Amer. Math. Soc., 347, 499–514 (1995). Article  MathSciNet  Google Scholar  A. Blokh, “Rotation numbers, twists and a Sharkovskii–Misiurewicz-type ordering for patterns on the interval,” Ergodic Theory Dynam. Syst., 15, 1–14 (1995). Article  MathSciNet  Google Scholar  A. Blokh, “On graph-realizable sets of periods,” J. Difference Equat. Appl., 9, 343–357 (2003). Article  MathSciNet  Google Scholar  A. Blokh and M. Misiurewicz, “New order for periodic orbits of interval maps,” Ergodic Theory Dynam. Syst., 17, 565–574 (1997). Article  MathSciNet  Google Scholar  A. Blokh and M. Misiurewicz, “Rotation numbers for certain maps of an n-od,” Topology Appl., 114, 27–48 (2001). Article  MathSciNet  Google Scholar  A. Blokh and M. Misiurewicz, “Forcing among patterns with no block structure,” Topology Proc., 54, 125–137 (2019). MathSciNet  Google Scholar  A. Blokh and M. Misiurewicz, “Renormalization towers and their forcing,” Trans. Amer. Math. Soc., 372, 8933–8953 (2019). Article  MathSciNet  Google Scholar  A. Blokh and O. M. Sharkovsky, “Sharkovsky ordering,” SpringerBriefs Math., Springer, Cham (2022). J. Bobok and M. Kuchta, “X-minimal patterns and a generalization of Sharkovskii’s theorem,” Fund. Math., 156, No. 1, 33–66 (1998). Article  MathSciNet  Google Scholar  A. Chenciner, J.-M. Gambaudo, and C. Tresser, “Une remarque sur la structure des endomorphismes de degré 1 du cercle,” C. R. Acad. Sci. Paris, Sér. I Math., 299, 145–148 (1984). L. S. Efremova, “Periodic orbits and the degree of a continuous map of a circle,” Different. Integral Equat. (Gorky), 2, 109–115 (1978). Google Scholar  R. Ito, “Rotation sets are closed,” Math. Proc. Cambridge Philos. Soc., 89, 107–111 (1981). Article  MathSciNet  Google Scholar  M. Misiurewicz, “Periodic points of maps of degree one of a circle,” Ergodic Theory Dynam. Syst., 2, 221–227 (1982). Article  MathSciNet  Google Scholar  M. Misiurewicz, “Formalism for studying periodic orbits of one dimensional maps,” in: Europ. Conf. on Iteration Theory (ECIT 87), World Scientific Publ. Co., Singapore (1989), pp. 1–7. S. Newhouse, J. Palis, and F. Takens, “Bifurcations and stability of families of diffeomorphisms,” Inst. Hautes Études Sci. Publ. Math., 57, 5–71 (1983). Article  MathSciNet  Google Scholar  H. Poincaré, “Sur les courbes définies par les équations différentielles,” Œuvres Complètes, 1, 137–158 (1952). Google Scholar  Scholarpedia article; http://www.scholarpedia.org/article/Rotation theory. A. N. Sharkovsky, “Co-existence of the cycles of a continuous mapping of the line into itself,” Ukr. Mat. Zh., 16, No. 1, 61–71 (1964). MathSciNet  Google Scholar  A. N. Sharkovsky, “Coexistence of the cycles of a continuous mapping of the line into itself,” Internat. J. Bifur. Chaos Appl. Sci. Eng., 5, 1263–1273 (1995). Article  Google Scholar  A. N. Sharkovsky, “On cycles and structure of a continuous map,” Ukr. Mat. Zh., 17, No. 3, 104–111 (1965). Google Scholar  K. Ziemian, “Rotation sets for subshifts of finite type,” Fundam. Math., 146, 189–201 (1995). Article  MathSciNet  Google Scholar  Download references Author information Authors and Affiliations Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA Alexander Blokh Department of Mathematical Sciences, Indiana University—Purdue University, Indianapolis, USA Michał Misiurewicz Authors Alexander BlokhView author publications Search author on:PubMed Google Scholar Michał MisiurewiczView author publications Search author on:PubMed Google Scholar Corresponding author Correspondence to Michał Misiurewicz. Additional information Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 1, pp. 48–61, January, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i1.7641. Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and permissions About this article Cite this article Blokh, A., Misiurewicz, M. Evolution of the Sharkovsky Theorem. Ukr Math J 76, 51–64 (2024). https://doi.org/10.1007/s11253-024-02306-x Download citation Received: 23 June 2023 Published: 30 July 2024 Version of record: 30 July 2024 Issue date: June 2024 DOI: https://doi.org/10.1007/s11253-024-02306-x Share this article Anyone you share the following link with will be able to read this content: Get shareable linkSorry, a shareable link is not currently available for this article. Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. Institutional subscriptions Advertisement Search Search by keyword or author Search Navigation Find a journal Publish with us Track your research Discover content Journals A-Z Books A-Z Publish with us Journal finder Publish your research Language editing Open access publishing Products and services Our products Librarians Societies Partners and advertisers Our brands Springer Nature Portfolio BMC Palgrave Macmillan Apress Discover Your privacy choices/Manage cookies Your US state privacy rights Accessibility statement Terms and conditions Privacy policy Help and support Legal notice Cancel contracts here 194.44.29.235 Not affiliated © 2026 Springer Nature
id umjimathkievua-article-7641
institution Ukrains’kyi Matematychnyi Zhurnal
keywords_txt_mv keywords
language English
last_indexed 2026-03-24T03:32:55Z
publishDate 2024
publisher Institute of Mathematics, NAS of Ukraine
record_format ojs
resource_txt_mv umjimathkievua/12/5598091bd9ee16ffccef88c619844312
spelling umjimathkievua-article-76412024-06-19T00:35:05Z Evolution of the Sharkovsky theorem Evolution of the Sharkovsky theorem Blokh, Alexander Misiurewicz, Michał Blokh, Alexander Misiurewicz, Michał the Sharkovsky Theorem UDC 517.9 We briefly describe some results that evolved from the Sharkovsky theorem. УДК 517.9 Еволюція теореми Шарковського  Коротко описано деякі результати, що розвинулися з теореми Шарковського. Institute of Mathematics, NAS of Ukraine 2024-02-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7641 10.3842/umzh.v76i1.7641 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 1 (2024); 48 - 61 Український математичний журнал; Том 76 № 1 (2024); 48 - 61 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7641/9678 Copyright (c) 2024 Michal Misiurewicz
spellingShingle Blokh, Alexander
Misiurewicz, Michał
Blokh, Alexander
Misiurewicz, Michał
Evolution of the Sharkovsky theorem
title Evolution of the Sharkovsky theorem
title_alt Evolution of the Sharkovsky theorem
title_full Evolution of the Sharkovsky theorem
title_fullStr Evolution of the Sharkovsky theorem
title_full_unstemmed Evolution of the Sharkovsky theorem
title_short Evolution of the Sharkovsky theorem
title_sort evolution of the sharkovsky theorem
topic_facet the Sharkovsky Theorem
url https://umj.imath.kiev.ua/index.php/umj/article/view/7641
work_keys_str_mv AT blokhalexander evolutionofthesharkovskytheorem
AT misiurewiczmichał evolutionofthesharkovskytheorem
AT blokhalexander evolutionofthesharkovskytheorem
AT misiurewiczmichał evolutionofthesharkovskytheorem

Ähnliche Einträge