scientific article

zbMath1103.32015MaRDI QIDQ3374875

Publication date: 27 February 2006

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

hypergeometric functions Riemann-Hilbert problem critical points differential Galois theory isomonodromic deformations Hodge structures abelian integrals holomorphic foliations Gauss-Manin connection isolated singularities Picard-Lefschetz theory Picard-Fuchs systems oscillating integrals monodromy theory regular and irregular singularities period mappings

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Period matrices, variation of Hodge structure; degenerations (32G20) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Singularities of vector fields, topological aspects (58K45) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Milnor fibration; relations with knot theory (32S55) Topological invariants on manifolds (58K65) Differential algebra (12H05) Deformations of complex singularities; vanishing cycles (32S30) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Critical points of functions and mappings on manifolds (58K05) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Monodromy on manifolds (58K10) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35)

Related Items (48)

Structurally stable nondegenerate singularities of integrable systems ⋮ Singularities of algebraic differential equations ⋮ The degree of the Gauss map of the theta divisor ⋮ Galois/Monodromy Groups for Decomposing Minimal Problems in 3D Reconstruction ⋮ Non-integrability of the Karabut system ⋮ Schlesinger equations for upper triangular matrices and their solutions ⋮ Polynomial dynamics and local analysis of small and grand orbits ⋮ Nonintegrability of Hamiltonian system perturbed from integrable system with two singular points ⋮ Periods of Hodge cycles and special values of the Gauss' hypergeometric function ⋮ The Hess-Appelrot system. III: Splitting of separatrices and chaos ⋮ Extended holonomy and topological invariance of vanishing holonomy group ⋮ The Poincaré center problem ⋮ Wildly ramified rigid G2$G_2$‐local systems ⋮ Perturbations of the Hess-Appelrot and the Lagrange cases in the rigid body dynamics ⋮ Tropical homology ⋮ On the integrability of Hamiltonian 1:2:2 resonance ⋮ Hamiltonian Monodromy via spectral Lax pairs ⋮ Topological actions of wreath products ⋮ The equivalence problem in analytic dynamics for 1-resonance ⋮ On the integrability of twofold 1 : 2 Hamiltonian resonance ⋮ Hodge-type structures as link invariants ⋮ Multiplicity of fixed points and growth of $\varepsilon $-neighborhoods of orbits ⋮ Unnamed Item ⋮ On the number of zeros of Melnikov functions ⋮ Unnamed Item ⋮ The Hess-Appelrot system. II: Perturbation and limit cycles ⋮ Linearised higher variational equations ⋮ First order linear differential equations with involutive delay and hypergeometric functions ⋮ On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields ⋮ Brieskorn module and center conditions: pull-back of differential equations in projective space ⋮ Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated ⋮ Painlevé equations, elliptic integrals and elementary functions ⋮ Linear differential equations and multiple zeta values. II: A generalization of the WKB method ⋮ On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem ⋮ Period integrals and mutation ⋮ Sliding invariants and classification of singular holomorphic foliations in the plane ⋮ A logic based approach to finding real singularities of implicit ordinary differential equations ⋮ The geometrical demonstration of the order of resonant saddle points in $\mathbb{C}^2$ ⋮ Contour integrals as Ad-invariant functions on the fundamental group ⋮ Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian ⋮ Heegaard Floer Homologies and Rational Cuspidal Curves. Lecture notes. ⋮ Analytic properties of the complete formal normal form for the Bogdanov–Takens singularity ^* ⋮ Some remarks on global analytic planar vector fields possessing an invariant analytic set ⋮ Linear differential systems with small coefficients: various types of solvability and their verification ⋮ Real Seifert Forms, Hodge Numbers and Blanchfield Pairings ⋮ The Hodge spectrum of analytic germs on isolated surface singularities ⋮ Catching Tangent Curves in Fields of Lines ⋮ On the classification of foliations of degree three with one singularity

This page was built for publication: