geometry of sets measures spaces fractals and rectifiability cambridge studies in advanced mathematics

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Geometry Of Sets And Measures In Euclidean Spaces

Author : Pertti Mattila
ISBN : 0521655951
Genre : Mathematics
File Size : 32. 50 MB
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This book studies the geometric properties of general sets and measures in euclidean space.

Fractured Fractals And Broken Dreams

Author : Guy David
ISBN : 0198501668
Genre : Mathematics
File Size : 72. 19 MB
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This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but thereis not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information."

Geometry And Analysis Of Fractals

Author : De-Jun Feng
ISBN : 9783662439203
Genre : Mathematics
File Size : 84. 39 MB
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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.

Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics

Author : David Carfi
ISBN : 9780821891476
Genre : Mathematics
File Size : 35. 51 MB
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This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Recent Developments In Fractals And Related Fields

Author : Julien Barral
ISBN : 9783319578057
Genre : Mathematics
File Size : 58. 12 MB
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This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Fourier Analysis And Hausdorff Dimension

Author : Pertti Mattila
ISBN : 9781107107359
Genre : Mathematics
File Size : 80. 32 MB
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Modern text examining the interplay between measure theory and Fourier analysis.

Taehan Suhakhoe Hoebo

Author :
ISBN : UOM:39015068671299
Genre : Mathematics
File Size : 70. 73 MB
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Bulletin Of The American Mathematical Society

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ISBN : UOM:49015003188621
Genre : Mathematics
File Size : 24. 87 MB
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Bulletin New Series Of The American Mathematical Society

Author :
ISBN : UOM:39015053360742
Genre : Mathematics
File Size : 70. 57 MB
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Nonautonomous Dynamical Systems

Author : Peter E. Kloeden
ISBN : 9780821868713
Genre : Mathematics
File Size : 61. 73 MB
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The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

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