Pseudoperiodic Topology
Pseudoperiodic Topology

Author: Vladimir Igorevich Arnolʹd

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 196

ISBN-13: 9780821820940

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This volume offers an account of the present state of the art in pseudoperiodic topology--a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting."

Pseudoperiodic Topology
Pseudoperiodic Topology

Author: Vladimir Igorevich Arnolʹd

Publisher:

Published: 1999

Total Pages:

ISBN-13: 9781470434083

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This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to s.

Pseudo-periodic Maps and Degeneration of Riemann Surfaces
Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Author: Yukio Matsumoto

Publisher: Springer

Published: 2011-08-17

Total Pages: 251

ISBN-13: 3642225349

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The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Pseudo-periodic Maps and Degeneration of Riemann Surfaces
Pseudo-periodic Maps and Degeneration of Riemann Surfaces

Author: Yukio Matsumoto

Publisher: Springer

Published: 2011-08-20

Total Pages: 240

ISBN-13: 9783642225352

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The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Handbook of Geometric Topology
Handbook of Geometric Topology

Author: R.B. Sher

Publisher: Elsevier

Published: 2001-12-20

Total Pages: 1145

ISBN-13: 0080532853

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Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

What's Next?
What's Next?

Author: Dylan Thurston

Publisher: Princeton University Press

Published: 2020-07-07

Total Pages: 472

ISBN-13: 0691185891

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William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas. This book brings together papers delivered by his colleagues and former students at "What's Next? The Mathematical Legacy of Bill Thurston," a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics—innovations that have had a profound and lasting impact on the mathematical community as a whole—and also features two papers based on Thurston's unfinished work in dynamics.

Topologies on Pseudo-Trees and Applications
Topologies on Pseudo-Trees and Applications

Author: Jacek Nikiel

Publisher: American Mathematical Soc.

Published: 1989

Total Pages: 126

ISBN-13: 0821824791

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A pseudo-tree is a partially ordered set such that the set of all predecessors of any element is linearly ordered. Clearly, each linearly ordered set is a pseudo-tree and pseudo-trees are, in general, much more complicated objects than chains. The aim of this paper is to develop a theory of natural order topologies on pseudo-trees which extends the theories of linearly ordered topological spaces and GO-spaces. Moreover, applications are given for some classes of continua which admit a natural ordering.

ARNOLD: Swimming Against the Tide
ARNOLD: Swimming Against the Tide

Author: Boris A. Khesin

Publisher: American Mathematical Society

Published: 2014-09-10

Total Pages: 221

ISBN-13: 1470416999

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Vladimir Arnold, an eminent mathematician of our time, is known both for his mathematical results, which are many and prominent, and for his strong opinions, often expressed in an uncompromising and provoking manner. His dictum that "Mathematics is a part of physics where experiments are cheap" is well known. This book consists of two parts: selected articles by and an interview with Vladimir Arnold, and a collection of articles about him written by his friends, colleagues, and students. The book is generously illustrated by a large collection of photographs, some never before published. The book presents many a facet of this extraordinary mathematician and man, from his mathematical discoveries to his daredevil outdoor adventures.

American Mathematical Society Translations
American Mathematical Society Translations

Author: United States. Office of Naval Research

Publisher: American Mathematical Soc.

Published: 2001-04-10

Total Pages: 268

ISBN-13: 9780821896051

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The articles in this collection present new results in combinatorics, algebra, algebraic geometry, dynamical systems, analysis, and probability. Of particular interest is the survey article by A. N. Kirillov devoted to combinatorics of Young diagrams and related problems of representation theory. Also included are articles devoted to the eightieth birthday of renowned Russian mathematician, V. A. Rokhlin, ``Remembrances of V. A. Rokhlin'', by I. R. Shafarevich, and ``An Unfinished Project of V.A. Rokhlin'', by V. N. Sudakov. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

Advanced Mathematical Methods in Biosciences and Applications
Advanced Mathematical Methods in Biosciences and Applications

Author: Faina Berezovskaya

Publisher: Springer Nature

Published: 2019-09-19

Total Pages: 268

ISBN-13: 3030157156

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Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.