Emerging Trends in Fractal Geometry and Dynamic Systems

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Geometry".

Deadline for manuscript submissions: 31 January 2027 | Viewed by 751

Special Issue Editors


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Guest Editor
School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, TX, USA
Interests: fractal geometry; dynamical systems; quantization; multifractal analysis; ergodic theory
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Guest Editor
School of Mathematics, Northwest University, Xi'an 710127, China
Interests: fractal geometry; dynamical systems; quantization; multifractal analysis; ergodic theory

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Guest Editor
School of Mathematics, Northwest University, Xi’an 710069, China
Interests: fractal geometry; dynamical systems; quantization; multifractal analysis; ergodic theory

Special Issue Information

Dear Colleagues,

This Special Issue aims to highlight recent advances and emerging directions in fractal geometry and dynamical systems, two closely connected fields with broad applications in mathematics, physics, data science, and nonlinear modeling. We seek high-quality research papers, short surveys, and expository works that reflect new ideas, techniques, and perspectives.

Topics of interest include:

- Fractals, self-similar sets, and dimension theory

- Iterated function systems and multifractal analysis

- Ergodic theory and invariant measures

- Dynamics on fractal sets and complex systems

- Quantization, geometric measure theory, and metric geometry

- Fractional dynamics and applications in physical and biological models

With rapid developments in geometric analysis, nonlinear dynamics, and fractal models, this Special Issue will provide a focused platform to disseminate cutting-edge research and foster collaboration across these interconnected areas. It will strengthen the journal’s role as a leading venue for work at the interface of fractal analysis and dynamical systems.

Prof. Dr. Mrinal Kanti Roychowdhury
Prof. Dr. Zhiming Li
Dr. Megha Pandey
Prof. Dr. María A. Navascués
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 250 words) can be sent to the Editorial Office for assessment.

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. Fractal and Fractional 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 2700 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

  • fractal geometry
  • multifractal analysis
  • geometric analysis
  • dynamical systems
  • fractal models
  • fractal sets
  • ergodic theory
  • measure theory

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Published Papers (1 paper)

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Research

18 pages, 318 KB  
Article
Multifractal Analysis of Unstable Polynomial Entropies in Partially Hyperbolic Systems
by Yangmei Mu and Lei Liu
Fractal Fract. 2026, 10(5), 310; https://doi.org/10.3390/fractalfract10050310 - 1 May 2026
Viewed by 336
Abstract
We investigate the multifractal structure of unstable local polynomial entropies for arbitrary Borel probability measures in partially hyperbolic dynamical systems. We introduce the notions of Bowen unstable polynomial entropy, unstable local polynomial entropy, and a measure-theoretic polynomial entropy in the unstable direction and [...] Read more.
We investigate the multifractal structure of unstable local polynomial entropies for arbitrary Borel probability measures in partially hyperbolic dynamical systems. We introduce the notions of Bowen unstable polynomial entropy, unstable local polynomial entropy, and a measure-theoretic polynomial entropy in the unstable direction and study their fundamental properties. Our main result establishes a multifractal relation for the level sets determined by unstable local polynomial entropies, showing that the Bowen unstable polynomial entropy of these sets is described by a Legendre-type formula involving the corresponding measure-theoretic polynomial entropy. Full article
(This article belongs to the Special Issue Emerging Trends in Fractal Geometry and Dynamic Systems)
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