Geometry And Dynamics
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The Principle Of Least Action In Geometry And Dynamics
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Author : Karl Friedrich Siburg
language : en
Publisher: Springer
Release Date : 2004-04-30
The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-30 with Mathematics categories.
New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Author : Marco Pettini
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics written by Marco Pettini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a “must” for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.
The Geometry Of Creation
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Author : Robert Bork
language : en
Publisher: Routledge
Release Date : 2016-12-05
The Geometry Of Creation written by Robert Bork and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-05 with History categories.
The flowering of Gothic architecture depended to a striking extent on the use of drawing as a tool of design. By drawing precise "blueprints" with simple tools such as the compass and straightedge, Gothic draftsmen were able to develop a linearized architecture of unprecedented complexity and sophistication. Examination of their surviving drawings can provide valuable and remarkably intimate information about the Gothic design process. Gothic drawings include compass pricks, uninked construction lines, and other telltale traces of the draftsman's geometrically based working method. The proportions of the drawings, moreover, are those actually intended by the designer, uncompromised by errors introduced in the construction process. All of these features make these drawings ideal subjects for the study of Gothic design practice, but their geometry has to date received little systematic attention. This book offers a new perspective on Gothic architectural creativity. It shows, in a series of rigorous geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labor, and across the centuries of the late Middle Ages. In each case study, a series of computer graphics show in unprecedented detail how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate both remarkable methodological continuity across the Gothic era, and the progressive development of new and sophisticated permutations on venerable design themes. This rich tradition ultimately gave way in the Renaissance not because of any inherent problem with Gothic architecture, but because the visual language of Classicism appealed more directly to the pretensions of Humanist princes than the more abstract geometrical order of Gothic design, as the book's final chapter demonstrates.
Dynamics Statistics And Projective Geometry Of Galois Fields
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Author : V. I. Arnold
language : en
Publisher:
Release Date : 2011
Dynamics Statistics And Projective Geometry Of Galois Fields written by V. I. Arnold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
V. I. Arnold reveals some unexpected connections between Galois fields and other apparently unrelated theories.
Geometry From Dynamics Classical And Quantum
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Author : José F. Cariñena
language : en
Publisher: Springer
Release Date : 2014-09-23
Geometry From Dynamics Classical And Quantum written by José F. Cariñena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Science categories.
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Fluids And Plasmas Geometry And Dynamics
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Author : Jerrold E. Marsden
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Fluids And Plasmas Geometry And Dynamics written by Jerrold E. Marsden and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
"The organizing committee envisioned bringing together three groups of people working on the following topics in fluid and plasma dynamics: 1. Geometric aspects : Hamiltonian structures, perturbation theory and nonlinear stability by variational methods, 2) Analytical and numerical methods: contour dynamics, spectral methods, and functional analytic techniques, 3) Dynamical systems aspects: experimental and numerical methods, bifurcation theory, and chaos."- introduction
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop
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Author : Lawrence Conlon
language : en
Publisher: World Scientific
Release Date : 2002-02-01
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop written by Lawrence Conlon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-01 with categories.
This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets.
Geometry Mechanics And Dynamics
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Author : Dong Eui Chang
language : en
Publisher: Springer
Release Date : 2015-04-16
Geometry Mechanics And Dynamics written by Dong Eui Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
Geometry And Topology In Dynamics
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Author : Marcy Barge
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Geometry And Topology In Dynamics written by Marcy Barge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.
Geometry Dynamics And Topology Of Foliations A First Course
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Author : Bruno Scardua
language : en
Publisher: World Scientific
Release Date : 2017-02-16
Geometry Dynamics And Topology Of Foliations A First Course written by Bruno Scardua and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-16 with Mathematics categories.
The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.