The Fuchsian theory of linear differential equations, which is named after Lazarus Immanuel Fuchs, provides a characterization of various types of singularities and the relations among them.
At any ordinary point of a homogeneous linear differential equation of order there exists a fundamental system of linearly independent power series solutions. A non-ordinary point is called a singularity. At a singularity the maximal number of linearly independent power series solutions may be less than the order of the differential equation.
The Fuchsiantheory of linear differential equations, which is named after Lazarus Immanuel Fuchs, provides a characterization of various types of singularities...
In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving...
to Bertrand in 1868. Clebsch (1873) attacked the theory along lines parallel to those in his theory of Abelian integrals. As the latter can be classified...
called Fuchsian equation or equation of Fuchsian type. For Fuchsian equations a formal fundamental system exists at any point, due to the Fuchsiantheory. Let...
hyperbolic plane. Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves...
listed as a grave of honour of the State of Berlin. He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation. A singular point a...
(1935) Fedoryuk, M. V. (2001) [1994], "Fuchsian equation", Encyclopedia of Mathematics, EMS Press A. R. Forsyth Theory of Differential Equations Vol. IV:...
developments of automorphic forms other than modular forms. The case of Γ a Fuchsian group had already received attention before 1900 (see below). The Hilbert...
just conjugate to Fuchsian groups under conformal transformations. Finitely generated quasi-Fuchsian groups are conjugate to Fuchsian groups under quasi-conformal...
Frobenius group Fuchsian group Geometric group theory Group action Homogeneous space Hyperbolic group Isometry group Orbit (group theory) Permutation Permutation...
the hyperbolic plane). Generalising the example of the modular group a Fuchsian group is a group admitting a properly discontinuous action on the hyperbolic...
Arithmetic Fuchsian groups are a special class of Fuchsian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic...
the areas of complex functions and differential equations. He studied Fuchsian functions of rank zero. He was interested in projective and non-Euclidean...
representation, is a Riemann–Hilbert problem. For a regular (and in particular Fuchsian) linear system one usually chooses as generators of the monodromy group...
of Kleinian models are in direct analogy to those of Fuchsian models; however, overall, the theory is less well developed. A number of unsolved conjectures...
contribution to the theory was made by Michio Jimbo, Tetsuji Miwa, and Kimio Ueno, who studied cases involving irregular singularities. A Fuchsian system is the...
arithmetic Fuchsian groups, and Teichmüller spaces. Fuchsian group Modular group Gamma Riemann surface Fuchsian model Analytic number theory Zoll surface...
groups Thompson's group F CAT(0) groups Arithmetic groups Automatic groups Fuchsian groups, Kleinian groups, and other groups acting properly discontinuously...
Möbius transformations, and its subgroups such as the modular group and Fuchsian group, based on work on automorphic functions in analysis. The abstract...
and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name field of definition. Fuchsian groups...
subgroup) Frieze group Wallpaper group Space group Crystallographic group Fuchsian group Modular group Congruence subgroup Kleinian group Discrete Heisenberg...
his Ph.D. (completed in 1974, awarded in 1975) on "The limit set of a Fuchsian group" under Alan Beardon. He spent 1974–1975 at Göttingen, 1975–1979 he...
a hundred research articles on theory of ordinary differential equations including Riemann–Hilbert problem and Fuchsian system. Bolibrukh was born on 30...
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