Singularities of Caustics and Wave Fronts


Author: Vladimir Arnold
Publisher: Springer Science & Business Media
ISBN: 9401133301
Category: Mathematics
Page: 259
View: 6404
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Real and Complex Singularities


Author: Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas
Publisher: American Mathematical Soc.
ISBN: 1470422050
Category: Differential geometry -- Classical differential geometry -- Classical differential geometry
Page: 355
View: 1230
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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)

Differential Geometry from a Singularity Theory Viewpoint


Author: Shyuichi E. T. Al IZUMIYA
Publisher: World Scientific
ISBN: 9814590452
Category: Mathematics
Page: 400
View: 5764
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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."--

Singularities of Differentiable Maps, Volume 1

Classification of Critical Points, Caustics and Wave Fronts
Author: V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher: Springer Science & Business Media
ISBN: 0817683402
Category: Mathematics
Page: 282
View: 8441
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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.

Geometry and Topology of Caustics -- Caustics ...


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Geometry, Differential
Page: N.A
View: 3097
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Успехи Математических Наук


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematicians
Page: N.A
View: 5981
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Journal of physics : A, Mathematical and general


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Science
Page: N.A
View: 3229
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Sūgaku Expositions

A Translation of Sūgaku
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6426
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Topological Invariants of Plane Curves and Caustics


Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
ISBN: 0821803085
Category: Mathematics
Page: 60
View: 1592
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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.

Symplectic singularities and geometry of gauge fields


Author: Robert Budzyński
Publisher: N.A
ISBN: N.A
Category: Science
Page: 403
View: 1430
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Sūri kagaku kōkyūroku


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2562
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Catastrophe Theory


Author: Vladimir I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 9783540548119
Category: Mathematics
Page: 150
View: 8760
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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.

Mathematical Methods of Classical Mechanics


Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Category: Mathematics
Page: 520
View: 521
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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.

Singularities and Oscillations


Author: Jeffrey Rauch,Michael Taylor
Publisher: Springer Science & Business Media
ISBN: 1461219728
Category: Science
Page: 158
View: 5539
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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


Author: Jean-Pierre Françoise,Gregory L. Naber,Sheung Tsun Tsou
Publisher: N.A
ISBN: 9780125126601
Category:
Page: 645
View: 1403
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Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation


Author: Alfredo Bermœdez
Publisher: SIAM
ISBN: 9780898714708
Category: Science
Page: 1038
View: 9390
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This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.

Advances in Microlocal Analysis


Author: H.G. Garnir
Publisher: Springer Science & Business Media
ISBN: 9789027721952
Category: Mathematics
Page: 390
View: 9870
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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.

Singularity Theory and Gravitational Lensing


Author: Arlie O. Petters,Harold Levine,Joachim Wambsganss
Publisher: Springer Science & Business Media
ISBN: 1461201454
Category: Science
Page: 603
View: 3867
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This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

Geometry and topology of caustics - Caustics '02


Author: Stanisław Janeczko,Dirk Siersma
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: 262
View: 6856
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Wavefronts and Rays as Characteristics and Asymptotics


Author: Andrej B¢na,Michael A. Slawinski
Publisher: World Scientific
ISBN: 9814295515
Category: Science
Page: 276
View: 1111
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This textbook ? incorporated with many illuminating examples and exercises ? is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation ? by a pure mathematician's standards ? is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and the phenomena such as caustics.