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Self Similar And Self Affine Sets And Measures
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Book Synopsis Self-similar and Self-affine Sets and Measures by : Balázs Bárány
Download or read book Self-similar and Self-affine Sets and Measures written by Balázs Bárány and published by American Mathematical Society. This book was released on 2023-11-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry of Sets and Measures in Euclidean Spaces by : Pertti Mattila
Download or read book Geometry of Sets and Measures in Euclidean Spaces written by Pertti Mattila and published by Cambridge University Press. This book was released on 1999-02-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.
Book Synopsis Fractal Geometry and Stochastics II by : Christoph Bandt
Download or read book Fractal Geometry and Stochastics II written by Christoph Bandt and published by Birkhäuser. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.
Book Synopsis Random Geometrically Graph Directed Self-Similar Multifractals by : Lars Olsen
Download or read book Random Geometrically Graph Directed Self-Similar Multifractals written by Lars Olsen and published by Routledge. This book was released on 2017-07-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multifractal theory was introduced by theoretical physicists in 1986. Since then, multifractals have increasingly been studied by mathematicians. This new work presents the latest research on random results on random multifractals and the physical thermodynamical interpretation of these results. As the amount of work in this area increases, Lars Olsen presents a unifying approach to current multifractal theory. Featuring high quality, original research material, this important new book fills a gap in the current literature available, providing a rigorous mathematical treatment of multifractal measures.
Book Synopsis Assouad Dimension and Fractal Geometry by : Jonathan M. Fraser
Download or read book Assouad Dimension and Fractal Geometry written by Jonathan M. Fraser and published by Cambridge University Press. This book was released on 2020-10-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Book Synopsis Geometry of Sets and Measures in Euclidean Spaces by : Pertti Mattila
Download or read book Geometry of Sets and Measures in Euclidean Spaces written by Pertti Mattila and published by Cambridge University Press. This book was released on 1999-02-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the geometric properties of general sets and measures in euclidean space.
Book Synopsis Fractals in Probability and Analysis by : Christopher J. Bishop
Download or read book Fractals in Probability and Analysis written by Christopher J. Bishop and published by Cambridge University Press. This book was released on 2017 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Book Synopsis Thermodynamic Formalism by : Mark Pollicott
Download or read book Thermodynamic Formalism written by Mark Pollicott and published by Springer Nature. This book was released on 2021-10-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler
Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Book Synopsis The Geometry of Fractal Sets by : K. J. Falconer
Download or read book The Geometry of Fractal Sets written by K. J. Falconer and published by Cambridge University Press. This book was released on 1985 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Book Synopsis Self-Similar Groups by : Volodymyr Nekrashevych
Download or read book Self-Similar Groups written by Volodymyr Nekrashevych and published by American Mathematical Society. This book was released on 2024-04-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-similar groups (groups generated by automata) appeared initially as examples of groups that are easy to define but that enjoy exotic properties like nontrivial torsion, intermediate growth, etc. The book studies the self-similarity phenomenon in group theory and shows its intimate relation with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. The relation is established through the notions of the iterated monodromy group and the limit space, which are the central topics of the book. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. It is shown in particular how Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties appear now not just as isolated examples but as naturally defined iterated monodromy groups of rational functions. The book is intended to be accessible to a wide mathematical readership, including graduate students interested in group theory and dynamical systems.
Book Synopsis Integral, Probability, and Fractal Measures by : Gerald A. Edgar
Download or read book Integral, Probability, and Fractal Measures written by Gerald A. Edgar and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.
Book Synopsis Fractals, Wavelets, and their Applications by : Christoph Bandt
Download or read book Fractals, Wavelets, and their Applications written by Christoph Bandt and published by Springer. This book was released on 2014-09-27 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Book Synopsis Geometry and Analysis of Fractals by : De-Jun Feng
Download or read book Geometry and Analysis of Fractals written by De-Jun Feng and published by Springer. This book was released on 2014-08-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
Book Synopsis Volume Doubling Measures and Heat Kernel Estimates on Self-Similar Sets by : Jun Kigami
Download or read book Volume Doubling Measures and Heat Kernel Estimates on Self-Similar Sets written by Jun Kigami and published by American Mathematical Soc.. This book was released on 2009-04-10 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the following three problems. 1. When does a measure on a self-similar set have the volume doubling property with respect to a given distance? 2. Is there any distance on a self-similar set under which the contraction mappings have the prescribed values of contractions ratios? 3. When does a heat kernel on a self-similar set associated with a self-similar Dirichlet form satisfy the Li-Yau type sub-Gaussian diagonal estimate? These three problems turn out to be closely related. The author introduces a new class of self-similar set, called rationally ramified self-similar sets containing both the Sierpinski gasket and the (higher dimensional) Sierpinski carpet and gives complete solutions of the above three problems for this class. In particular, the volume doubling property is shown to be equivalent to the upper Li-Yau type sub-Gaussian diagonal estimate of a heat kernel.
Book Synopsis Challenges for the 21st Century by : Louis H. Y. Chen
Download or read book Challenges for the 21st Century written by Louis H. Y. Chen and published by World Scientific. This book was released on 2001-05-08 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Fundamental Sciences: Mathematics and Theoretical Physics provided a forum for reviewing some of the significant developments in mathematics and theoretical physics in the 20th century; for the leading theorists in these fields to expound and discuss their views on new ideas and trends in the basic sciences as the new millennium approached; for increasing public awareness of the importance of basic research in mathematics and theoretical physics; and for promoting a high level of interest in mathematics and theoretical physics among school students and teachers. This was a major conference, with invited lectures by some of the leading experts in various fields of mathematics and theoretical physics.
Book Synopsis Fractal Geometry and Stochastics V by : Christoph Bandt
Download or read book Fractal Geometry and Stochastics V written by Christoph Bandt and published by Birkhäuser. This book was released on 2015-07-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.
