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Fractals
Fractals are not just a matter of geometry but have a number of applications for the well-being of life. Fractal properties are useful in medical...
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Fractals
This book is about mathematical beauty. Usually, when I think of beauty in mathematics, I’m thinking of elegance and simplicity. However, in...
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Topological properties of fractals via M-polynomial
Sierpiński graphs are frequently related to fractals, and fractals apply in several fields of science, i.e., in chemical graph theory, computer...
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Geodesic metrics on fractals and applications to heat kernel estimates
It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ , then the new motion (the time-changed...
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Fractals via Self-Similar Group of Fisher Contractions
The fractal notion was unveiled by Mandelbrot in 1975, and a number of researchers continued to popularize the fractal theory. The chaotic structures...
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Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances
This paper introduces an equivalent condition for the existence of regular local irreducible conservative Dirichlet forms that are self-similar under...
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From Strichartz Estimates to Differential Equations on Fractals
Robert Strichartz made a substantial impact on analysis via his deep and original results in classical harmonic, functional, and spectral analysis...
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Fractals and Dimensions
In Euclidean geometry, any smooth curve is one-dimensional and any smooth surface is two-dimensional. It is not the case when we encounter with...
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About Sobolev spaces on fractals: fractal gradians and Laplacians
The paper covers the foundations of fractal calculus on fractal curves, defines different function classes, establishes vector spaces for
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Generation of fractals by \(\Phi\)-iterated tupling system
The purpose of this paper is to present new m -tuple fractals using strong m -tuple fixed point method, which provides a positive answer to the...
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An Application of Viscosity Approximation Type Iterative Method in the Generation of Mandelbrot and Julia Fractals
In this paper, we present an application of the viscosity approximation type iterative method introduced by Nandal et al. (Iteration Process for...
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Random walks, spectral gaps, and Khintchine’s theorem on fractals
This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor’s...
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Fractals, Narrative, and Cognition
Joseph Campbell’s theory of the “monomyth” posits a narrative deep structure underlying all human storytelling. In his words, the monomyth represents...
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Heat Kernel Fluctuations for Stochastic Processes on Fractals and Random Media
It is well known that stochastic processes on fractal spaces or in certain random media exhibit anomalous heat kernel behaviour. One manifestation of...
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Homogeneous Dirichlet Forms on p.c.f. Fractals and their Spectral Asymptotics
We formulate a class of “homogeneous” Dirichlet forms (DF) that aims to explore those forms that do not satisfy the conventional energy self-similar...
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From Classical Analysis to Analysis on Fractals A Tribute to Robert Strichartz, Volume 1
Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original...
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Fractional Gaussian fields on the Sierpiński Gasket and related fractals
We study the regularity of the Gaussian random measures (− Δ) − s W on the Sierpiński gasket where W is a white noise and Δ the Laplacian with respect...
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Fractional Fractals
This paper introduces the notion of “fractional fractals”. The main idea is to establish a connection between the classical iterated function system...
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Rauzy Fractals and their Number-Theoretic Applications
In this paper, we construct and study Rauzy partitions of order n for a certain class of Pisot numbers. These partitions are partitions of a torus...