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140122 ||| eng |
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|a 9789401102131
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|a Vassiliev, V.A.
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|a Ramified Integrals, Singularities and Lacunas
|h Elektronische Ressource
|c by V.A. Vassiliev
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| 250 |
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|a 1st ed. 1995
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1995, 1995
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| 300 |
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|a XVII, 294 p
|b online resource
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|a § 4. Description of the small monodromy group -- § 5. Proof of Main Theorem 3 -- IV. Lacunas and the local Petrovski
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|a § 6. Sharpness implies the local Petrovskii condition close to discrete-type points of wave fronts of strictly hyperbolic operators -- § 7. The local Petrovskii condition may be stronger than the sharpness close to singular points not of discrete type -- § 8. Normal forms of nonsharpness close to singularities of wave fronts (after A.N. Varchenko) -- § 9. Several problems -- V. Calculation of local Petrovski
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|a § 8. A program for counting topologically different morsifications of a real singularity -- § 9. More detailed description of the algorithm -- Appendix: a FORTRAN program searching for the lacunas and enumerating the morsifications of real function singularities
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|a I. Picard—Lefschetz—Pham theory and singularity theory -- § 1. Gauss-Manin connection in the homological bundles. Monodromy and variation operators -- § 2. The Picard-Lefschetz formula. The Leray tube operator -- § 3. Local monodromy of isolated singularities of holomorphic functions -- § 4. Intersection form and complex conjugation in the vanishing homology of real singularities in two variables -- § 5. Classification of real and complex singularities of functions -- § 6. Lyashko-Looijenga covering and its generalizations -- § 7. Complements of discriminants of real simple singularities (after E. Looijenga) -- § 8. Stratifications. Semialgebraic, semianalytic and subanalytic sets -- § 9. Pham’s formulae -- § 10. Monodromy of hyperplane sections -- § 11. Stabilization of local monodromy and variation of hyperplane sections close to strata of positive dimension (stratified Picard-Lefschetz theory) --
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|a § 12. Homology of local systems. Twisted Picard-Lefschetz formulae -- § 13. Singularities of complete intersections and their local monodromy groups -- II. Newton’s theorem on the nonintegrability of ovals -- § 1. Stating the problems and the main results -- § 2. Reduction of the integrability problem to the (generalized) PicardLefschetz theory -- § 3. The element “cap” -- § 4. Ramification of integration cycles close to nonsingular points. Generating functions and generating families of smooth hypersurfaces -- § 5. Obstructions to integrability arising from the cuspidal edges. Proof of Theorem 1.8 -- § 6. Obstructions to integrability arising from the asymptotic hyperplanes. Proof of Theorem 1.9 -- § 7. Several open problems -- III. Newton’s potential of algebraic layers -- § 1. Theorems of Newton and Ivory -- § 2. Potentials of hyperbolic layers are polynomialin the hyperbolicity domains (after Arnold and Givental) -- § 3. Proofs of Main Theorems 1 and 2 --
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|a Algebraic Geometry
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|a Mathematical analysis
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|a Potential theory (Mathematics)
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|a Integral Transforms and Operational Calculus
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|a Manifolds and Cell Complexes
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|a Algebraic geometry
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|a Manifolds (Mathematics)
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|a Differential Equations
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|a Potential Theory
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|a Differential equations
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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|a Mathematics and Its Applications
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|a 10.1007/978-94-011-0213-1
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| 856 |
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|u https://doi.org/10.1007/978-94-011-0213-1?nosfx=y
|x Verlag
|3 Volltext
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|a 515.72
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