The Theory of Singularities and Its Applications

The Theory of Singularities and Its Applications PDF

Author: Vladimir Igorevich Arnolʹd

Publisher: Cambridge University Press

Published: 1991-05-31

Total Pages: 88

ISBN-13: 9780521422802

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In this book, which is based on lectures given in Pisa under the auspices of the Accademia Nazionale dei Lincei, the distinguished mathematician Vladimir Arnold describes those singularities encountered in different branches of mathematics. He avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear, such as geometry and optics; optimal control theory and algebraic geometry; reflection groups and dynamical systems and many more. This will be an excellent companion for final year undergraduates and graduates whose area of study brings them into contact with singularities.

Theory of Singularities and Its Applications

Theory of Singularities and Its Applications PDF

Author: Vladimir Igorevich Arnolʹd

Publisher:

Published: 1990

Total Pages: 346

ISBN-13: 9781470445485

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The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and.

Introduction to Singularities and Deformations

Introduction to Singularities and Deformations PDF

Author: Gert-Martin Greuel

Publisher: Springer Science & Business Media

Published: 2007-02-23

Total Pages: 482

ISBN-13: 3540284192

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Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Dynamical Systems VI

Dynamical Systems VI PDF

Author: Vladimir Igorevich Arnold

Publisher: Springer Science & Business Media

Published: 1993

Total Pages: 264

ISBN-13: 9783540505839

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'EMS 6' is the latest volume in the sub series 'Dynamical Systems of the Encyclopaedia'. It is the first of two volumes covering Singularity Theory, which, besides its fundamental use in Dynamical Systems and Bifurcation Theory, is an important part of other fields such as algebraic geometry, differential geometry and geometric optics.

Singularities of Caustics and Wave Fronts

Singularities of Caustics and Wave Fronts PDF

Author: Vladimir Arnold

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 271

ISBN-13: 9401133301

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One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Intersection Homology & Perverse Sheaves

Intersection Homology & Perverse Sheaves PDF

Author: Laurenţiu G. Maxim

Publisher: Springer Nature

Published: 2019-11-30

Total Pages: 270

ISBN-13: 3030276449

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This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Tight Closure and Its Applications

Tight Closure and Its Applications PDF

Author: Craig Huneke

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 152

ISBN-13: 082180412X

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This monograph deals with the theory of tight closure and its applications. The contents are based on ten talks given at a CBMS conference held at North Dakota State University in June 1995.

Singularity Theory and its Applications

Singularity Theory and its Applications PDF

Author: David Mond

Publisher: Springer

Published: 2006-11-14

Total Pages: 416

ISBN-13: 3540470603

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A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.

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