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Embedding Problems In Symplectic Geometry
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Book Synopsis Embedding Problems in Symplectic Geometry by : Felix Schlenk
Download or read book Embedding Problems in Symplectic Geometry written by Felix Schlenk and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
Book Synopsis Holomorphic Curves in Symplectic Geometry by : Michele Audin
Download or read book Holomorphic Curves in Symplectic Geometry written by Michele Audin and published by Birkhäuser. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.
Book Synopsis Complex and Symplectic Geometry by : Daniele Angella
Download or read book Complex and Symplectic Geometry written by Daniele Angella and published by Springer. This book was released on 2017-10-12 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Book Synopsis Symplectic Geometry by : Helmut Hofer
Download or read book Symplectic Geometry written by Helmut Hofer and published by Springer Nature. This book was released on 2022-12-05 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Book Synopsis Dynamics, Ergodic Theory and Geometry by : Boris Hasselblatt
Download or read book Dynamics, Ergodic Theory and Geometry written by Boris Hasselblatt and published by Cambridge University Press. This book was released on 2007-09-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.
Book Synopsis Topological Persistence in Geometry and Analysis by : Leonid Polterovich
Download or read book Topological Persistence in Geometry and Analysis written by Leonid Polterovich and published by American Mathematical Soc.. This book was released on 2020-05-11 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Book Synopsis The Restricted Three-Body Problem and Holomorphic Curves by : Urs Frauenfelder
Download or read book The Restricted Three-Body Problem and Holomorphic Curves written by Urs Frauenfelder and published by Springer. This book was released on 2018-08-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Symplectic Geometry by : A.T. Fomenko
Download or read book Symplectic Geometry written by A.T. Fomenko and published by CRC Press. This book was released on 1995-11-30 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Alexander Cardona
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by Cambridge University Press. This book was released on 2013-05-09 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.
Book Synopsis Introduction to Symplectic Topology by : Dusa McDuff
Download or read book Introduction to Symplectic Topology written by Dusa McDuff and published by Oxford University Press. This book was released on 2017 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. This new third edition of a classic book in the feild includes updates and new material to bring the material right up-to-date.
Download or read book What's Next? written by Dylan Thurston and published by Princeton University Press. This book was released on 2020-07-07 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Lagrangian Torus Fibrations by : Jonny Evans
Download or read book Lectures on Lagrangian Torus Fibrations written by Jonny Evans and published by Cambridge University Press. This book was released on 2023-07-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Book Synopsis Symplectic Geometry and Topology by : Yakov Eliashberg
Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Book Synopsis Stability Analysis of Impulsive Functional Differential Equations by : Ivanka Stamova
Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009-10-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Book Synopsis Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes by : De Gosson Maurice A
Download or read book Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes written by De Gosson Maurice A and published by World Scientific. This book was released on 2017-11-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical. Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field. Contents: Hamiltonian MechanicsHamilton–Jacobi TheoryMatter Waves, Schrödinger's Equation, and Bohm's Theory The MetatronUncertainties and Quantum BlobsQuantum States and the Density MatrixVarying Planck's ConstantAppendices: The Symplectic GroupThe Metaplectic RepresentationBorn–Jordan QuantizationTwisted Product and Convolution Readership: Undergraduate and graduate students of mathematics and physics, interested in analysis and differential equations, probability and statistics, geometry and topology and mathematical physics. Keywords: Classical Mechanics;Hamiltonian Mechanics;Quantum Mechanics;Planck's Constant;Mathematical Physics;Algebraic GeometryReview:0
Book Synopsis Products of Finite Groups by : Adolfo Ballester-Bolinches
Download or read book Products of Finite Groups written by Adolfo Ballester-Bolinches and published by Walter de Gruyter. This book was released on 2010-10-19 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of finite groups factorised as a product of two or more subgroups has become a subject of great interest during the last years with applications not only in group theory, but also in other areas like cryptography and coding theory. It has experienced a big impulse with the introduction of some permutability conditions. The aim of this book is to gather, order, and examine part of this material, including the latest advances made, give some new approach to some topics, and present some new subjects of research in the theory of finite factorised groups. Some of the topics covered by this book include groups whose subnormal subgroups are normal, permutable, or Sylow-permutable, products of nilpotent groups, and an exhaustive structural study of totally and mutually permutable products of finite groups and their relation with classes of groups. This monograph is mainly addressed to graduate students and senior researchers interested in the study of products and permutability of finite groups. A background in finite group theory and a basic knowledge of representation theory and classes of groups is recommended to follow it.
