Pseudoperiodic Topology
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| Author | : Vladimir Igorevich Arnolʹd |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 196 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821820940 |
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."
| Author | : V. M. Buchstaber |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780821836132 |
The second half of the 20th century and its conclusion : crisis in the physics and mathematics community in Russia and in the West -- Interview with Sergey P. Novikov -- The w-function of the KdV hierarchy -- On the zeta functions of a meromorphic germ in two variables -- On almost duality for Frobenius manifolds -- Finitely presented semigroups in knot theory. Oriented case -- Topological robotics : subspace arrangements and collision free motion planning -- The initial-boundary value problem on the interval for the nonlinear Schrödinger equation. The algebro-geometric approach. I -- On odd Laplace operators. II -- From 2D Toda hierarchy to conformal maps for domains of the Riemann sphere --Integrable chains on algebraic curves -- Fifteen years of KAM for PDE -- Graded filiform Lie algebras and symplectic nilmanifolds --Adiabatic limit in the Seiberg-Witten equations -- Affine Krichever-Novikov algebras, their representations and applications -- Tame integrals of motion and o-minimal structures.
| Author | : Dylan Thurston |
| Publisher | : Princeton University Press |
| Total Pages | : 437 |
| Release | : 2020-07-07 |
| Genre | : Mathematics |
| ISBN | : 0691185891 |
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.
| Author | : Faina Berezovskaya |
| Publisher | : Springer Nature |
| Total Pages | : 268 |
| Release | : 2019-09-19 |
| Genre | : Mathematics |
| ISBN | : 3030157156 |
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.
| Author | : Boris A. Khesin |
| Publisher | : American Mathematical Society |
| Total Pages | : 221 |
| Release | : 2014-09-10 |
| Genre | : Mathematics |
| ISBN | : 1470416999 |
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.
| Author | : United States. Office of Naval Research |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 268 |
| Release | : 2001-04-10 |
| Genre | : Mathematics |
| ISBN | : 9780821896051 |
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.
| Author | : V. M. Buchstaber |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 408 |
| Release | : 2014-11-18 |
| Genre | : Mathematics |
| ISBN | : 1470418711 |
Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
| Author | : 野水克己 |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 152 |
| Release | : 2003 |
| Genre | : Differential equations, Partial |
| ISBN | : 9780821835081 |
This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.
| Author | : Oleg N. Karpenkov |
| Publisher | : Springer Nature |
| Total Pages | : 462 |
| Release | : 2022-05-28 |
| Genre | : Mathematics |
| ISBN | : 3662652773 |
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
| Author | : R.B. Sher |
| Publisher | : Elsevier |
| Total Pages | : 1145 |
| Release | : 2001-12-20 |
| Genre | : Mathematics |
| ISBN | : 0080532853 |
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.
