Search results for "Affine coordinate system"
showing 5 items of 5 documents
Darstellung von Hyperebenen in verallgemeinerten affinen Räumen durch Moduln
1994
The starting point of this article is a generalized concept of affine space which includes all affine spaces over unitary modules. Our main result is a representation theorem for hyperplanes of affine spaces: Every hyperplane which satisfies a weak richness condition is induced by a module. 1
The coordinatization of affine planes by rings
1996
With every unitary free module of rank 2 there is naturally associated a generalized affine plane (e.g. the lines are just the cosets of all nonzero 1-generated submodules). Here we solve the converse problem by coordinatizing a given generalized affine plane which satisfies certain versions of Desargues' postulate.
Genericity of dimension drop on self-affine sets
2017
We prove that generically, for a self-affine set in $\mathbb{R}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
On invariant measures of finite affine type tilings
2006
In this paper, we consider tilings of the hyperbolic 2-space, built with a finite number of polygonal tiles, up to affine transformation. To such a tiling T, we associate a space of tilings: the continuous hull Omega(T) on which the affine group acts. This space Omega(T) inherits a solenoid structure whose leaves correspond to the orbits of the affine group. First we prove the finite harmonic measures of this laminated space correspond to finite invariant measures for the affine group action. Then we give a complete combinatorial description of these finite invariant measures. Finally we give examples with an arbitrary number of ergodic invariant probability measures.
Affine Kettengeometrien �ber Jordanalgebren
1996
It is shown that an affine chain geometry over a Jordan algebra can be constructed in a nearly classical manner. Conversely, such chain geometries are characterized as systems of rational normal curves having a group of automorphisms with certain properties.