Self Similar And Self Affine Sets And Measures
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Author | : Balázs Bárány |
Publisher | : American Mathematical Society |
Total Pages | : 466 |
Release | : 2023-11-16 |
Genre | : Mathematics |
ISBN | : 1470470462 |
Download Self-similar and Self-affine Sets and Measures Book in PDF, Epub and Kindle
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.
Author | : Sirakov Boyan |
Publisher | : World Scientific |
Total Pages | : 5396 |
Release | : 2019-02-27 |
Genre | : Mathematics |
ISBN | : 9813272899 |
Download Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) Book in PDF, Epub and Kindle
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author | : Pertti Mattila |
Publisher | : Cambridge University Press |
Total Pages | : 358 |
Release | : 1999-02-25 |
Genre | : Mathematics |
ISBN | : 1316583694 |
Download Geometry of Sets and Measures in Euclidean Spaces Book in PDF, Epub and Kindle
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.
Author | : Christoph Bandt |
Publisher | : Birkhäuser |
Total Pages | : 286 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034883803 |
Download Fractal Geometry and Stochastics II Book in PDF, Epub and Kindle
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.
Author | : Pertti Mattila |
Publisher | : Cambridge University Press |
Total Pages | : 360 |
Release | : 1999-02-25 |
Genre | : Mathematics |
ISBN | : 9780521655958 |
Download Geometry of Sets and Measures in Euclidean Spaces Book in PDF, Epub and Kindle
This book studies the geometric properties of general sets and measures in euclidean space.
Author | : Christopher J. Bishop |
Publisher | : Cambridge University Press |
Total Pages | : 415 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 1107134110 |
Download Fractals in Probability and Analysis Book in PDF, Epub and Kindle
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Author | : Jonathan M. Fraser |
Publisher | : Cambridge University Press |
Total Pages | : 287 |
Release | : 2020-10-29 |
Genre | : Mathematics |
ISBN | : 1108478654 |
Download Assouad Dimension and Fractal Geometry Book in PDF, Epub and Kindle
The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.
Author | : Lars Olsen |
Publisher | : Routledge |
Total Pages | : 268 |
Release | : 2017-07-12 |
Genre | : Mathematics |
ISBN | : 1351419862 |
Download Random Geometrically Graph Directed Self-Similar Multifractals Book in PDF, Epub and Kindle
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.
Author | : Mark Pollicott |
Publisher | : Springer Nature |
Total Pages | : 536 |
Release | : 2021-10-01 |
Genre | : Mathematics |
ISBN | : 3030748634 |
Download Thermodynamic Formalism Book in PDF, Epub and Kindle
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.
Author | : K. J. Falconer |
Publisher | : Cambridge University Press |
Total Pages | : 184 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : 9780521337052 |
Download The Geometry of Fractal Sets Book in PDF, Epub and Kindle
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.