Fractals, Dynamical Systems, and Nonlinear Functional Analysis
Journal of Nonlinear Functional Analysis welcomes submissions to the Topical Collection on “Fractals, Dynamical Systems, and Nonlinear Functional Analysis” edited by Bilel Selmi (University of Monastir, Tunisia; [email protected]), Zhiming Li (Northwest University, China; [email protected]), and María Navascués (University of Zaragoza, Spain; [email protected]).
Fractals are intricate geometric shapes that can be split into parts, each of which is a reduced-scale copy of the whole. This property is known as self-similarity. Fractals are not only fascinating mathematical objects but also appear in nature, modeling phenomena like coastlines, mountain ranges, and even biological systems such as bronchial trees. The study of fractals involve the understanding of their dimensions, typically non-integer (or fractal) dimensions, which provide insight into their complexity and scaling properties. Dynamical systems theory is a branch of mathematics used to describe the behavior of complex systems over time. These systems can be defined by a set of rules or equations, which dictate how the state of the system evolves. Examples include the solar system, weather patterns, and population dynamics. Dynamical systems can exhibit a range of behaviors from simple and predictable to chaotic and unpredictable. Studying these systems helps us understand stability, bifurcations, and long-term behavior. Nonlinear functional analysis is a field of mathematics that deals with non-linear mappings and their properties in infinite-dimensional spaces. This area extends the classical functional analysis, which mainly deals with linear operators. Nonlinear functional analysis is crucial to solving differential equations, optimization problems, and understanding the structure of function spaces. Key concepts include fixed-point theorems, variational methods, and the study of nonlinear operators. Most of the fractals arise as attractors of dynamical systems. For instance, the Mandelbrot set and Julia sets are generated by iterating complex functions. Studying these fractals provides insights into the stability and bifurcation properties of the underlying dynamical systems. The behavior of dynamical systems, especially those described by differential equations, often involves nonlinearities. Nonlinear functional analysis provides the tools to analyze these systems, helping to prove the existence and uniqueness of solutions, study their stability, and understand long-term behavior. The study of fractals often involves nonlinear processes. Nonlinear functional analysis helps in the understanding of the properties of functions and operators that describe fractal structures. For example, fixed point theorems in nonlinear functional analysis are used to prove the existence of fractal attractors in dynamical systems. In summary, the interplay between fractals, dynamical systems, and nonlinear functional analysis enables a deeper understanding of complex phenomena, providing powerful mathematical frameworks to model, analyze, and predict the behavior of intricate systems. This synergy has broad applications across physics, biology, economics, and beyond, making it a cornerstone of modern mathematical research. The special issue aims to explore the mathematical aspects of fractal dimensions, functions, and measures. It will feature high-quality contributions from global experts, covering topics such as dimension theory, ergodic theory, dynamical systems, fractional calculus, and their interplay with fractal geometry. Articles will highlight recent advances in fractal concepts and their practical utility in numerical analysis, fractional calculus, approximation theory, quantization theory, fixed-point theorems, variational methods and more. Ultimately, the special issue seeks to unite scientists, including emerging researchers, to share insights and contribute papers on fractal dimensions, functions, measures, and dynamical systems.
The thematic series will accept for publications high-quality research papers on the following topics
• Fractals in Physics
• Complex Systems
• Fractal Functions with Applications
• Numerical Techniques
• Mathematical Physics on Fractals
• Fractal Dimension
• Quantization Theory
• Iterated Functions Systems
• Fractional Calculus
• Multifractal Analysis
• Approximation Theory
• Fixed-point Theory
• Variational Methods
• Iteration Theory, Iterative and Composite Equations
• Nonsmooth Analysis
• Convex Analysis and Their Applications
• Ergodic Theory
• Self-similar Sets and Measures
Authors have to prepare the manuscript according to template of our journal (download the template here). Manuscripts should be submitted by one of the authors of the manuscript through the online Manuscript Tracking System, MTS. There is no page limit. If for some technical reason submission through the MTS is not possible, the author can submit their papers by email (PDF format) to a member of the Guest Editors with a cc to [email protected].