Assouad Dimension And Fractal Geometry
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Assouad Dimension And Fractal Geometry
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Author : Jonathan M. Fraser
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-29
Assouad Dimension And Fractal Geometry written by Jonathan M. Fraser and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-29 with Mathematics categories.
The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Fractal Geometry And Stochastics Vi
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Author : Uta Freiberg
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Fractal Geometry And Stochastics Vi written by Uta Freiberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.
Thermodynamic Formalism
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Author : Mark Pollicott
language : en
Publisher: Springer Nature
Release Date : 2021-10-01
Thermodynamic Formalism written by Mark Pollicott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Recent Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Springer Nature
Release Date : 2025-04-18
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Mathematics categories.
This volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals. It includes both original research contributions, as well as surveys from many of the leading experts on modern fractal geometry theory and applications. The contributions contained in the book stem from the conference “Fractals and Related Fields IV", that was held in 2022 on the Island of Porquerolles, France. Various aspects of fractal geometry in connection with harmonic analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, functional analysis, additive combinatorics, embedding theory, and signal and image processing are addressed within its pages. We hope that the book will be interesting for pure and applied mathematicians in these areas, as well as for other researchers curious to discover more about fractals.
An Invitation To Fractal Geometry
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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-30
An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.
This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.
Some Novel Types Of Fractal Geometry
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Author : Stephen Semmes
language : en
Publisher: Oxford University Press
Release Date : 2001
Some Novel Types Of Fractal Geometry written by Stephen Semmes and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincaré inequalities, concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than has been realized. Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features. 'Some Novel Types of Fractal Geometry' will be of interest to graduate students and researchers in mathematics, working in various aspects of geometry and analysis.
Coarse Geometry Of Topological Groups
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Author : Christian Rosendal
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Coarse Geometry Of Topological Groups written by Christian Rosendal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Mathematics categories.
Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
The Mordell Conjecture
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Author : Hideaki Ikoma
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-03
The Mordell Conjecture written by Hideaki Ikoma and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.
This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) and a concise introduction to Diophantine geometry.
Self Similar And Self Affine Sets And Measures
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Author : Balázs Bárány
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-16
Self Similar And Self Affine Sets And Measures written by Balázs Bárány and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Mathematics categories.
Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.
Attractors Of Hamiltonian Nonlinear Partial Differential Equations
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Author : Alexander Komech
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-30
Attractors Of Hamiltonian Nonlinear Partial Differential Equations written by Alexander Komech and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-30 with Mathematics categories.
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.