Fuchsian group - Wikipedia
网页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 isometries of the hyperbolic plane , or conformal transformations of the unit disc, or conformal transformations of the upper half plane , so a Fuchsian group can be regarded as a group ...
线性ODE的一般理论和黎曼-希尔伯特对应 - 知乎
网页Fuchsian系统就是形如 D \bold{y} = A \bold{y} 的系统，其中 A 的输入都取在 \mathbb{C}(z) 里，且对任何 P\in \mathbb{P}_1 都是系统的常点或正则奇点。 设 S = \{p_1,\cdots ,p_r\} 是所有有限大的奇点，则存在常数矩阵 A_1,\cdots ,A_r ，使得
网页set of discrete subgroups of PSL2(R), or Fuchsian Groups. Fuchsian Groups are particularly important to the areas of hyperbolic geometry of Riemann surfaces and algebraic curves. 1. Hyperbolic Geometry The hyperbolic plane is obtained by maintaining that all of Euclid’s axioms are true with the exception of the parallel postulate, which is ...
富克斯群：20世纪组合学与几何群论的重要里程碑
网页2023年7月26日 · 富克斯群(Fuchsian group)是指一类离散的子群，作为特殊线性群PSL(2, R)在上半平面H上的作用群。 它由所有能够通过仿射变换和椭圆变换将上半平面H映射到自身的矩阵组成。
Fuchsian group - Encyclopedia of Mathematics
网页2023年3月15日 · Fuchsian group. A discrete group of holomorphic transformations (cf. Discrete group of transformations) of an (open) disc $ K $ onto the Riemann sphere, that is, of a disc or a half-plane onto the complex plane. Most often one takes for $ …
网页2 Fuchsian groups. In this section we will provide a few equivalent characterizations of the term "Fuchsian group". Fuchsian group is a discrete subgroup of PSL(2, R). Fuchsian group is a group that acts properly discontinuously on the upper half plane.
Fuchsian Groups, Katok - The University of Chicago Press
网页This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential ...
网页In order to find all elementary Fuchsian groups we first consider an arbitrary Fuchsian group G which leaves ~ invariant and which fixes a single point w. The fixed points of elliptic elements cannot occur on a~: the fixed points of parabolic and hyperbolic elements of G must occur on a~.
Fuchsian Group -- from Wolfram MathWorld
网页2024年8月22日 · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
Fuchsian Groups - Svetlana Katok - Google Books
网页A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry,...
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