Cylinder decomposition veech surface

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August undefined, 2024

WebAmerican Mathematical Society :: Homepage WebThe trace eld of a Veech surface (X;!) is Q(tr A : A 2SL(X;!)) is the smallest eld extension of Q that contains the trace of all elements of SL(X;!). 1 For an appropriately scaled …

Notes on the Veech group of the Chamanara surface - arXiv

WebThe Veech group of the surface is the subgroup of SL(2,R) consisting of elements that map the surface to itself by this action. I will describe a method for computing elements of the Veech group. ... • A multi-curve on a surface produces a decomposition of the surface into cylinders. Thus a parabolic automorphism of the surface may be ... WebA cylinder decomposition of (X,A) is a collection of maximal cylinders in (X,A) so that the closures of the cylinders in Xcover Xand so that each two cylinders are disjoint. We … debelah morgan close to you mp3 download

Notes on the Veech group of the Chamanara surface – arXiv Vanity

WebMay 31, 2010 · We study infinite translation surfaces which are $\ZZ$-covers of finite square-tiled surfaces obtained by a certain two-slit cut and paste construction.We show that if the finite translation surface has a one-cylinder decomposition in some direction, then the Veech group of the infinite translation surface is either a lattice or an infinitely … WebA Veech surface is an \exceptionally symmetric" translation surface, in the sense that the Veech group is a ( nite co-volume) lattice in SL(2;R) (it is easily seen that the Veech group is never co-compact). Simple examples of Veech sur-faces are square-tiled surfaces, obtained by gluing nitely many copies of the unit WebJun 18, 2024 · In the first case, there is only one cylinder decomposition because any other decomposition would contain a closed geodesic that would cross every cylinder … debeka rathenow

WEAK MIXING DIRECTIONS IN NON-ARITHMETIC VEECH …

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Webclosure of a translation surface and the cylinders on the translation surface. The Siegel-Veech formula establishes such a connection asymp-totically in counting problems [Vee98,EM01]. The Veech Dichotomy shows in particular that for translation surfaces in closed orbits, a very strong form of complete peri-odicity holds [Vee89]. http://homepages.math.uic.edu/~masur/chm-rv.pdf fear of failure effects on sports performanceWebsurface is called Veech if the image of this homomorphism is a lattice. Even when the surface is not Veech, it has some interesting automorphisms. ... rise to a horizontal cylinder decomposition on the surface. Each cylinder is shaded a di erent color. De nition 2.6. For us, an isosceles trapezoid is a vertically symmetric ... debe ir al médico 2 2 of 7

"WebThe non-Veech case of Theorem1.2is proved very similarly to Theorem1.1. Finally we have some additional results on polygonal area when q is a Veech surface. The ﬁrst of these will be derived from the analogous result for VT(q) in [SW10]. Theorem1.3. If q is a Veech surface then Poly(q) is a discrete subset of R. Next, for a ¨0 deﬁne the ... " - Cylinder decomposition veech surface

Cylinder decomposition veech surface

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WebA novelty of our implementation is a subroutine that uses Delaunay triangulations to e ciently decompose a Veech surface (X;!) into cylinders in the direction of any saddle … WebDownload scientific diagram Cylinder decomposition of the double pentagon surface. One cylinder is white; the other is shaded from publication: Cutting sequences, regular polygons, and the Veech ...

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http://www-personal.umich.edu/~alexmw/Cylinder.pdf WebAug 17, 2004 · the direction v, the surface decomposes as a union of cylinders. A surface S is completely periodic if any direction in which there is at least one cylinder of closed …

WebThe height of the cylinder is the width W W of the rectangular label. So the area of the label can be represented as. To find the total surface area of the cylinder, we add the areas … Webdecomposes into cylinders in that direction and a surface (X,ω) is said to be completely periodic, if any direction that has some cylinder in that direction is completely periodic. Calta ([Ca]) showed that in genus 2, if the holonomy ﬁeld lies in a quadratic extension of Q, then if the surface is not a Veech surface, it is completely periodic.

WebDec 19, 2016 · Theorem 1.1. Let S be a Veech surface in 7i(2) which cannot be rescaled so that p(Hi(S,Z)) cQxQ. Let v be a completely periodic direction for S. Suppose the cylinder decompositon in the direction v has two cylinders. Let Wi,w2,hi,h2,ti,t2 be the widths, heights and twists of these two cylinders. The twists are measured WebLet S be a Veech surface in H(2) which cannot be rescaled so that p(H 1(S,Z)) ⊂ Q× Q. Let v be a completely periodic direction for S. Suppose the cylinder decompositon in the direction v has two cylinders. Let w1,w2,h1,h2,t1,t2 be the widths, heights and twists of these two cylinders.

Webs = translation_surfaces.veech_double_n_gon(5) It is best to work in the field in which the surfact is defined. p=s.polygon(0) p Polygon: (0, 0), (1, 0), (1/2*a^2 - 1/2, 1/2*a), (1/2, 1/2*a^3 - a), (-1/2*a^2 + 3/2, 1/2*a) The surface has a horizontal cylinder decomposition all of whose moduli are given as below

WebA cylinder diagram encodes the combinatorics of cylinder decomposition of a completely periodic direction in a translation surface. If we adjoin coordinates to this combinatorial datum, we have a complete description of the underlying surface. In the case of arithmetic curves, the coordinates can be taken to be rational numbers. debe j owens wright debe high schoolWebAug 28, 2024 · Figure 12. A cylinder decomposition of the surface of genus $ 2 $ Figure 13. A dilation torus, which is not a Hopf torus Figure 14. A dilation surface with a non … debek public school lebanonmWebA Veech surface is arithmeticif it is a covering of a ﬂat torus, ramiﬁed over one point; otherwise, it is a non-arithmetic Veech surface. 2.2. Classiﬁcation of Veech surfaces … fear of failure in schoolWebJun 18, 2024 · Theorem 1.2 is proved in Sect. 3. Horizon saddle connections constrain the action of $SL(2,\mathbb {R})$.In the following, the Veech group V(X) of a dilation surface X is the stabilizer of the action of $SL(2,\mathbb {R})$.There is a remarkable similarity with the three types of Veech groups for translation surfaces with poles: continuous, cyclic … debelah morgan dance with me mp3 downloadWebsuch a cylinder never exits it which is incompatible with the fact that a trian-gulated surface deprived of its 1-skeleton is a union of triangles. A remarkable … debelah morgan dance with me album downloadWebcore(X) decomposes into a (maybe empty) family of cylinders of commensurablemoduli. Otherwise,theSL(2,R)-orbitof(X,q) isnotclosedintheambientstratum. ... In strata of dimension one, the Veech group of ev-ery surface is of continuous type. In strata of dimension at least three, the Veech group of a generic surface is trivial. In strata of ... fear of failure in children