Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.9
Journals
Axioms
Special Issues
Topological Theory of Dynamical Systems
share announcement

Topological Theory of Dynamical Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 6527

Special Issue Editors

Prof. Dr. Kazuhiro Sakai

E-Mail Website
Guest Editor
Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan
Interests: shadowing property; dynamical systems theory; bifurcation theory; ergodic theory; vector fields; chaos theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Naoya Sumi

E-Mail
Guest Editor
Department of Mathematics, Kumamoto University, Kumamoto 860-8555, Japan
Interests: dynamical systems and ergodic theory

Special Issue Information

Dear Colleagues,

Since Anosov and Bowen's works, the topological theory of uniformly hyperbolic dynamical systems was rapidly developed, and many fruitful results have been obtained. Topological theory based on non-uniformly hyperbolic dynamical systems is also now developing, and the results obtained in these studies usually play important parts in both the qualitative theory of dynamical systems and the numerical theory of dynamical systems.

This Special Issue will stimulate the study of dynamical systems to explore the new directions and further developments, by collecting recent achievements in the modern topological theory of dynamical systems from the dynamical systems community around the world. Achievements in differentiable settings are also welcome and it is expected that new development in topological theory will be inspired by such research papers.

For this Special Issue, we are particularly seeking contributions on the following three topics:

Topological theory of dynamical systems based on the frameworks of uniformly hyperbolic and non-uniformly hyperbolic dynamical systems (the results in differentiable settings are also welcome).

Topological theory of dynamical systems intertwined with measure theory, ergodic theory, chaos theory, probability theory, combinatorics, and so on.

Survey articles that present significant (new or not so new) open questions on the topological theory of dynamical systems.

Prof. Dr. Kazuhiro Sakai
Dr. Naoya Sumi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Topological dynamical systems
  • Uniformly hyperbolic
  • Structurally stable
  • Topologically stable
  • Non-uniformly hyperbolic
  • Partially hyperbolic
  • Dominated splitting
  • Singular hyperbolic
  • Shadowing property
  • Shadowable measure
  • Expansive
  • Plaque expansive
  • Expansive measure
  • Iterated function system
  • Ergodic theory
  • Random dynamical system
  • Chaos theory
  • Probability theory
  • Combinatorics

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Related Special Issue

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

13 pages, 3558 KiB  
Article
Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps
by Sergey Kryzhevich, Viktor Avrutin, Nikita Begun, Dmitrii Rachinskii and Khosro Tajbakhsh
Axioms 2021, 10(2), 80; https://doi.org/10.3390/axioms10020080 - 2 May 2021
Cited by 2 | Viewed by 2341
Abstract
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the parameters of the system. These results were [...] Read more.
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally. Full article
(This article belongs to the Special Issue Topological Theory of Dynamical Systems)
►▼ Show Figures

Figure 1

7 pages, 252 KiB  
Article
Trees in Positive Entropy Subshifts
by Ville Salo
Axioms 2021, 10(2), 77; https://doi.org/10.3390/axioms10020077 - 29 Apr 2021
Cited by 2 | Viewed by 1504
Abstract
I give a simple proof for the fact that positive entropy subshifts contain infinite binary trees where branching happens synchronously in each branch, and that the branching times form a set with positive lower asymptotic density. Full article
(This article belongs to the Special Issue Topological Theory of Dynamical Systems)
7 pages, 244 KiB  
Article
Filtrated Pseudo-Orbit Shadowing Property and Approximately Shadowable Measures
by Kazuhiro Sakai and Naoya Sumi
Axioms 2021, 10(1), 38; https://doi.org/10.3390/axioms10010038 - 20 Mar 2021
Cited by 1 | Viewed by 1947
Abstract
In this paper, it is proved that every diffeomorphism possessing the filtrated pseudo-orbit shadowing property admits an approximately shadowable Lebesgue measure. Furthermore, the C1-interior of the set of diffeomorphisms possessing the filtrated pseudo-orbit shadowing property is characterized as the set of [...] Read more.
In this paper, it is proved that every diffeomorphism possessing the filtrated pseudo-orbit shadowing property admits an approximately shadowable Lebesgue measure. Furthermore, the C1-interior of the set of diffeomorphisms possessing the filtrated pseudo-orbit shadowing property is characterized as the set of diffeomorphisms satisfying both Axiom A and the no-cycle condition. As a corollary, it is proved that there exists a C1-open set of diffeomorphisms, any element of which does not have the shadowing property but admits an approximately shadowable Lebesgue measure. Full article
(This article belongs to the Special Issue Topological Theory of Dynamical Systems)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop