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Diffeology


Diffeology
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Diffeology


Diffeology
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Author : Patrick Iglesias-Zemmour
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09

Diffeology written by Patrick Iglesias-Zemmour 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 2013-04-09 with Mathematics categories.


Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, co-products, subsets, limits, and co-limits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject.



The Moment Maps In Diffeology


The Moment Maps In Diffeology
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Author : Patrick Iglesias-Zemmour
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

The Moment Maps In Diffeology written by Patrick Iglesias-Zemmour 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 2010 with Mathematics categories.


"This memoir presents a generalization of the moment maps to the category {Diffeology}. This construction applies to every smooth action of any diffeological group G preserving a closed 2-form w, defined on some diffeological space X. In particular, that reveals a universal construction, associated to the action of the whole group of automorphisms Diff (X, w). By considering directly the space of momenta of any diffeological group G, that is the space g* of left-invariant 1-forms on G, this construction avoids any reference to Lie algebra or any notion of vector fields, or does not involve any functional analysis. These constructions of the various moment maps are illustrated by many examples, some of them originals and others suggested by the mathematical literature."--Publisher's description.



New Spaces In Mathematics


New Spaces In Mathematics
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Author : Mathieu Anel
language : en
Publisher: Cambridge University Press
Release Date : 2021-04

New Spaces In Mathematics written by Mathieu Anel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04 with Mathematics categories.


In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.



Recent Advances In Diffeologies And Their Applications


Recent Advances In Diffeologies And Their Applications
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Author : Jean-Pierre Magnot
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-02

Recent Advances In Diffeologies And Their Applications written by Jean-Pierre Magnot and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-02 with Mathematics categories.


This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.



Nonlinear Systems And Their Remarkable Mathematical Structures


Nonlinear Systems And Their Remarkable Mathematical Structures
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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2019-12-06

Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.


Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 2 is written in a careful pedagogical manner by experts from the field of nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). This book aims to clearly illustrate the mathematical theories of nonlinear systems and its progress to both non-experts and active researchers in this area. Just like the first volume, this book is suitable for graduate students in mathematics, applied mathematics and engineering sciences, as well as for researchers in the subject of differential equations and dynamical systems. Features Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-experts Suitable for a broad readership including researchers and graduate students in mathematics and applied mathematics



Current Trends In Analysis Its Applications And Computation


Current Trends In Analysis Its Applications And Computation
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Author : Paula Cerejeiras
language : en
Publisher: Springer Nature
Release Date : 2022-10-03

Current Trends In Analysis Its Applications And Computation written by Paula Cerejeiras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-03 with Mathematics categories.


This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.



Infinite Dimensional Lie Groups In Geometry And Representation Theory


Infinite Dimensional Lie Groups In Geometry And Representation Theory
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Author : Augustin Banyaga
language : en
Publisher: World Scientific
Release Date : 2002-07-12

Infinite Dimensional Lie Groups In Geometry And Representation Theory written by Augustin Banyaga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-12 with Science categories.


This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics.



Programming Languages And Systems


Programming Languages And Systems
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Author : Nobuko Yoshida
language : en
Publisher: Springer Nature
Release Date : 2021-03-22

Programming Languages And Systems written by Nobuko Yoshida and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-22 with Computers categories.


This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems.



Geometry And Topology Of Manifolds


Geometry And Topology Of Manifolds
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Author : Jan Kubarski
language : en
Publisher:
Release Date : 2007

Geometry And Topology Of Manifolds written by Jan Kubarski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Manifolds (Mathematics) categories.




Smooth Homotopy Of Infinite Dimensional C Infty Manifolds


Smooth Homotopy Of Infinite Dimensional C Infty Manifolds
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Author : Hiroshi Kihara
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-27

Smooth Homotopy Of Infinite Dimensional C Infty Manifolds written by Hiroshi Kihara and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-27 with Mathematics categories.


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