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Mathematics
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Advances in Ergodic Theory and Its Applications
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Advances in Ergodic Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 4430

Special Issue Editors

Dr. Claudio Bonanno

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Guest Editor
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, I-56127 Pisa, Italy
Interests: transfer operators and thermodynamic formalism; infinite measure preserving systems; links with number theory
Prof. Dr. Jorge Milhazes Freitas

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Guest Editor
Centro de Matemática and Faculdade de Ciências da Universidade do Porto Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Interests: statistical properties of dynamical systems; extreme value theory; recurrence and hitting times; limit theorems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ana Cristina Moreira Freitas

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Guest Editor
Faculdade de Economia, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Interests: extreme value theory; recurrence and hitting times; point processes; dynamically generated stochastic processes
Prof. Dr. Marco Lenci

E-Mail Website
Guest Editor
1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
Interests: infinite ergodic theory; statistical properties of dynamical systems; billiards; random walks; applications to physical systems

Special Issue Information

Dear Colleagues,

Ergodic theory is the branch of dynamical systems that studies the probabilistic and statistical aspects of the orbits of a system, which has been a very active field of research in recent years. In this Issue, we aim to collect contributions providing new and interesting results in the field, as well as applications to other branches of mathematics (e.g., number theory and probability theory). Applications to other fields of science (e.g., modeling of phenomena in physics, biology, and economics) will also be considered if the results include a theoretical understanding of the models presented.

Dr. Claudio Bonanno
Prof. Dr. Jorge Milhazes Freitas
Prof. Dr. Ana Cristina Moreira Freitas
Prof. Dr. Marco Lenci
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • statistical properties of dynamical systems
  • links to other branches of mathematics
  • properties of systems modeling phenomena in other sciences

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Published Papers (2 papers)

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Research

16 pages, 342 KiB  
Article
On the Generalised Transfer Operators of the Farey Map with Complex Temperature
by Claudio Bonanno
Mathematics 2023, 11(1), 134; https://doi.org/10.3390/math11010134 - 27 Dec 2022
Viewed by 1329
Abstract
We consider the problem of showing that 1 is an eigenvalue for a family of generalised transfer operators of the Farey map. This is an important problem in the thermodynamic formalism approach to dynamical systems, which in this particular case is related to [...] Read more.
We consider the problem of showing that 1 is an eigenvalue for a family of generalised transfer operators of the Farey map. This is an important problem in the thermodynamic formalism approach to dynamical systems, which in this particular case is related to the spectral theory of the modular surface via the Selberg Zeta function and the theory of dynamical zeta functions of maps. After briefly recalling these connections, we show that the problem can be formulated for operators on an appropriate Hilbert space and translated into a linear algebra problem for infinite matrices. This formulation gives a new way to study numerically the spectrum of the Laplace–Beltrami operator and the properties of the Selberg Zeta function for the modular surface. Full article
(This article belongs to the Special Issue Advances in Ergodic Theory and Its Applications)
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15 pages, 308 KiB  
Article
Collective Sensitivity, Collective Accessibility, and Collective Kato’s Chaos in Duopoly Games
by Hongqing Wang, Tianxiu Lu, Risong Li, Yuanlin Chen, Yongjiang Li and Weizhen Quan
Mathematics 2022, 10(22), 4226; https://doi.org/10.3390/math10224226 - 12 Nov 2022
Cited by 1 | Viewed by 1163
Abstract
By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction [...] Read more.
By using the uniform continuity of two onto maps, this paper further explores stronger forms of Kato’s chaos, sensitivity, and accessibility of Cournot maps. In particular, the sensitivity, the collective sensitivity, the accessibility, and the collective accessibility of the compositions of two reaction functions are studied. It is observed that a Cournot onto map H on a product space is sensitive (collectively sensitive, collectively accessible, accessible, or collectively Kato chaotic) if and only if the restriction of the map H2 to the MPE-set is sensitive as well. Several examples are given to show the necessity of the reaction functions being continuous onto maps. Full article
(This article belongs to the Special Issue Advances in Ergodic Theory and Its Applications)
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