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Singularities of Caustics and Wave Fronts

Singularities of Caustics and Wave Fronts Author Vladimir Arnold
ISBN-10 9789401133302
Release 2013-12-01
Pages 259
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Singularities of Differentiable Maps Volume 1

Singularities of Differentiable Maps  Volume 1 Author V.I. Arnold
ISBN-10 9780817683405
Release 2012-05-24
Pages 282
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​Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.



Differential Geometry from a Singularity Theory Viewpoint

Differential Geometry from a Singularity Theory Viewpoint Author Shyuichi E. T. Al IZUMIYA
ISBN-10 9789814590457
Release 2015-10-29
Pages 400
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"Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces."--



Arnold s Problems

Arnold s Problems Author Vladimir I. Arnold
ISBN-10 3540206140
Release 2004-06-24
Pages 640
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Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research



Catastrophe Theory

Catastrophe Theory Author Vladimir I. Arnol'd
ISBN-10 9783642581243
Release 2012-12-06
Pages 150
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The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.



Real and Complex Singularities

Real and Complex Singularities Author Ana Claudia Nabarro
ISBN-10 9781470422059
Release 2016-10-25
Pages 355
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This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)



Topological Invariants of Plane Curves and Caustics

Topological Invariants of Plane Curves and Caustics Author Vladimir Igorevich Arnolʹd
ISBN-10 9780821803080
Release 1994
Pages 60
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This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.



S gaku Expositions

S  gaku Expositions Author
ISBN-10 UOM:39015057375126
Release 2002
Pages
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S gaku Expositions has been writing in one form or another for most of life. You can find so many inspiration from S gaku Expositions also informative, and entertaining. Click DOWNLOAD or Read Online button to get full S gaku Expositions book for free.



Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics Author V.I. Arnol'd
ISBN-10 9781475720631
Release 2013-04-09
Pages 520
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.



Solitons geometry and topology

Solitons  geometry  and topology Author Arkadiĭ Anatolʹevich Malʹt︠s︡ev
ISBN-10 UCSC:32106015563817
Release 1999
Pages 381
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Solitons geometry and topology has been writing in one form or another for most of life. You can find so many inspiration from Solitons geometry and topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Solitons geometry and topology book for free.



Geometry and Topology of Caustics Caustics

Geometry and Topology of Caustics    Caustics    Author
ISBN-10 UOM:39015060925537
Release 2006
Pages
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Singularities and Oscillations

Singularities and Oscillations Author Jeffrey Rauch
ISBN-10 9781461219729
Release 2012-12-06
Pages 158
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This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary, to the examination of viscous boundary layers. It examines the foundations of the theory of high- frequency electromagnetic waves in a dielectric or semiconducting medium. Nor are unifying themes entirely absent from nonlinear analysis: one chapter considers microlocal analysis, including paradifferential operator calculus, on Morrey spaces, and connections with various classes of partial differential equations.



Encyclopedia of mathematical physics

Encyclopedia of mathematical physics Author Jean-Pierre Françoise
ISBN-10 0125126603
Release 2006
Pages 645
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Encyclopedia of mathematical physics has been writing in one form or another for most of life. You can find so many inspiration from Encyclopedia of mathematical physics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Encyclopedia of mathematical physics book for free.



Soviet Physics Uspekhi

Soviet Physics  Uspekhi Author
ISBN-10 UCSD:31822017887902
Release 1984
Pages
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Soviet Physics Uspekhi has been writing in one form or another for most of life. You can find so many inspiration from Soviet Physics Uspekhi also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Soviet Physics Uspekhi book for free.



Advances in Microlocal Analysis

Advances in Microlocal Analysis Author H.G. Garnir
ISBN-10 9027721955
Release 1986-02-28
Pages 390
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The 1985 Castel vecchio-Pas coli NATO Advanced Study Institute is aimed to complete the trilogy with the two former institutes I organized : "Boundary Value Problem for Evolution Partial Differential Operators", Liege, 1976 and "Singularities in Boundary Value Problems", Maratea, 1980. It was indeed necessary to record the considerable progress realized in the field of the propagation of singularities of Schwartz Distri butions which led recently to the birth of a new branch of Mathema tical Analysis called Microlocal Analysis. Most of this theory was mainly built to be applied to distribution solutions of linear partial differential problems. A large part of this institute still went in this direction. But, on the other hand, it was also time to explore the new trend to use microlocal analysis In non linear differential problems. I hope that the Castelvecchio NATO ASI reached its purposes with the help of the more famous authorities in the field. The meeting was held in Tuscany (Italy) at Castelvecchio-Pascoli, little village in the mountains north of Lucca on September 2-12, 1985. It was hosted by "11 Ciocco" an international vacation Center, In a comfortable hotel located in magnificent mountain surroundings and provided with all conference and sport facilities.



Geometry and topology of caustics Caustics 02

Geometry and topology of caustics   Caustics  02 Author Stanisław Janeczko
ISBN-10 CORNELL:31924098844248
Release 2004
Pages 262
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Russian Mathematical Surveys

Russian Mathematical Surveys Author
ISBN-10 UCAL:B3627730
Release 1975
Pages
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Russian Mathematical Surveys has been writing in one form or another for most of life. You can find so many inspiration from Russian Mathematical Surveys also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Russian Mathematical Surveys book for free.