On Some Aspects Of The Theory Of Anosov Systems

Author : Grigorii A. Margulis
Publisher : Springer Science & Business Media
Page : 144 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662090701

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On Some Aspects of the Theory of Anosov Systems by Grigorii A. Margulis Pdf

The seminal 1970 Moscow thesis of Grigoriy A. Margulis, published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 46,5 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : Cesar E. Silva,Alexandre I. Danilenko
Publisher : Springer Nature
Page : 707 pages
File Size : 46,8 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781071623886

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Ergodic Theory by Cesar E. Silva,Alexandre I. Danilenko Pdf

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
Page : 712 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662070017

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Elementary and Analytic Theory of Algebraic Numbers by Wladyslaw Narkiewicz Pdf

This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.

Author : David Fisher,Dmitry Kleinbock,Gregory Soifer
Publisher : University of Chicago Press
Page : 573 pages
File Size : 47,6 Mb
Release : 2022-02-07
Category : Mathematics
ISBN : 9780226804163

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Dynamics, Geometry, Number Theory by David Fisher,Dmitry Kleinbock,Gregory Soifer Pdf

This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.

Author : David E. Edmunds,William D. Evans
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 51,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662077313

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Hardy Operators, Function Spaces and Embeddings by David E. Edmunds,William D. Evans Pdf

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

Author : Vladimir Kanovei,Michael Reeken
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 44,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662089989

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Nonstandard Analysis, Axiomatically by Vladimir Kanovei,Michael Reeken Pdf

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

Author : Friedrich Ischebeck,Ravi A. Rao
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 53,9 Mb
Release : 2005-11-22
Category : Mathematics
ISBN : 9783540263708

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Ideals and Reality by Friedrich Ischebeck,Ravi A. Rao Pdf

Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

Author : A.D. Alexandrov
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 51,9 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540263401

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Convex Polyhedra by A.D. Alexandrov Pdf

This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 49,6 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

Author : Anonim
Publisher : World Scientific
Page : 1001 pages
File Size : 51,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf

Author : Nicolau Corção Saldanha
Publisher : American Mathematical Soc.
Page : 247 pages
File Size : 49,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846285

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Foliations, Geometry, and Topology by Nicolau Corção Saldanha Pdf

Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.

Author : R. J. Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 51,5 Mb
Release : 2009-01-29
Category : Mathematics
ISBN : 9780387481166

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Random Fields and Geometry by R. J. Adler,Jonathan E. Taylor Pdf

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

Author : Boris Hasselblatt
Publisher : Springer
Page : 334 pages
File Size : 45,7 Mb
Release : 2017-12-15
Category : Mathematics
ISBN : 9783319430591

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Ergodic Theory and Negative Curvature by Boris Hasselblatt Pdf

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.

Author : Helge Holden,Ragni Piene
Publisher : Springer Nature
Page : 876 pages
File Size : 42,8 Mb
Release : 2024
Category : Computer science
ISBN : 9783031339738

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The Abel Prize 2018-2022 by Helge Holden,Ragni Piene Pdf

The book presents the winners of the Abel Prize in mathematics for the period 2018-2022: - Robert P. Langlands (2018) - Karen K. Uhlenbeck (2019) - Hillel Furstenberg and Gregory Margulis (2020) - Lászlo Lóvász and Avi Wigderson (2021) - Dennis P. Sullivan (2022) The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos from the period 2018-2022 showing many of the additional activities connected with the Abel Prize. This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer, 2014) as well as on The Abel Prize 2013-2017 (Springer, 2019), which profile the previous Abel Prize laureates.