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Dynamical And Spectral Applications Of Gromov Hausdorff Theory
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Book Synopsis Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs by : Jihoon Lee
Download or read book Gromov-Hausdorff Stability of Dynamical Systems and Applications to PDEs written by Jihoon Lee and published by Springer Nature. This book was released on 2022-10-30 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents new insights into the perturbation theory of dynamical systems based on the Gromov-Hausdorff distance. In the first part, the authors introduce the notion of Gromov-Hausdorff distance between compact metric spaces, along with the corresponding distance for continuous maps, flows, and group actions on these spaces. They also focus on the stability of certain dynamical objects like shifts, global attractors, and inertial manifolds. Applications to dissipative PDEs, such as the reaction-diffusion and Chafee-Infante equations, are explored in the second part. This text will be of interest to graduates students and researchers working in the areas of topological dynamics and PDEs.
Book Synopsis Gromov-Hausdorff Topology and Its Applications to Riemannian Manifolds by : Dong-Pyo Chi
Download or read book Gromov-Hausdorff Topology and Its Applications to Riemannian Manifolds written by Dong-Pyo Chi and published by . This book was released on 1998 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry of Dynamical Triangulations by : Jan Ambjorn
Download or read book The Geometry of Dynamical Triangulations written by Jan Ambjorn and published by Springer Science & Business Media. This book was released on 2009-02-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.
Book Synopsis Modern Dynamical Systems and Applications by : Michael Brin
Download or read book Modern Dynamical Systems and Applications written by Michael Brin and published by Cambridge University Press. This book was released on 2004-08-16 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.
Book Synopsis Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by : Tushar Das
Download or read book Geometry and Dynamics in Gromov Hyperbolic Metric Spaces written by Tushar Das and published by American Mathematical Soc.. This book was released on 2017-04-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Book Synopsis Noncommutative Geometry and Optimal Transport by : Pierre Martinetti
Download or read book Noncommutative Geometry and Optimal Transport written by Pierre Martinetti and published by American Mathematical Soc.. This book was released on 2016-10-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
Book Synopsis Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance by : Marc Aristide Rieffel
Download or read book Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance written by Marc Aristide Rieffel and published by American Mathematical Soc.. This book was released on 2004 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di
Book Synopsis American Doctoral Dissertations by :
Download or read book American Doctoral Dissertations written by and published by . This book was released on 2002 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Applications of the Bochner-Martinelli Integral by : A. M. Kytmanov
Download or read book Some Applications of the Bochner-Martinelli Integral written by A. M. Kytmanov and published by . This book was released on 1999 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of International Workshop on Mathematical and Physical Aspects of Nonlinear Field Theories by : Dongho Chae
Download or read book Proceedings of International Workshop on Mathematical and Physical Aspects of Nonlinear Field Theories written by Dongho Chae and published by . This book was released on 1998 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ergodic Theory and Negative Curvature by : Boris Hasselblatt
Download or read book Ergodic Theory and Negative Curvature written by Boris Hasselblatt and published by Springer. This book was released on 2017-12-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.
Book Synopsis The Proceedings of the Conference[s] on Geometric Structures on Manifolds by : Suhyoung Choi
Download or read book The Proceedings of the Conference[s] on Geometric Structures on Manifolds written by Suhyoung Choi and published by . This book was released on 1999 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lecture Notes on the Global Stability of the Minkowski Space by : Francesco Nicolò
Download or read book Lecture Notes on the Global Stability of the Minkowski Space written by Francesco Nicolò and published by . This book was released on 2000 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Notes on Boundary Values in Ultradistribution Spaces by : Richard D. Carmichael
Download or read book Notes on Boundary Values in Ultradistribution Spaces written by Richard D. Carmichael and published by . This book was released on 1999 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari
Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Book Synopsis Type III Factors and Index Theory by : Hideki Kosaki
Download or read book Type III Factors and Index Theory written by Hideki Kosaki and published by . This book was released on 1998 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Classification of Manifolds by : Steven Hutt
Download or read book Introduction to the Classification of Manifolds written by Steven Hutt and published by . This book was released on 2000 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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