Cylinder decomposition veech surface

Author: kaqt

August undefined, 2024

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 WebThe surface obtained by identifying opposite sides of a regular hexagon is also a torus,asmaybeseenbycomputingtheEulercharacteristic: onetwo-cell(thehexagon …

A short introduction to translation surfaces, Veech surfaces, …

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 … WebDepartment of Mathematics The University of Chicago cts boss turbo

CYLINDER DEFORMATIONS IN ORBIT CLOSURES OF …

Webbecause a surface in a ﬁxed stratum can have arbitrarily many short saddle connections (for instance, by taking a surface with a short slit, and then gluing in a cylinder with small height and circumference). But, according to Theorem 1.2, as we increase R, the effect of these short saddle connections eventually diminishes. WebAug 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 … 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 … cts bottom dump

Finding the Volume and Surface Area of a Cylinder Prealgebra

Pascal Hubert and Thomas Schmidt October 26, 2004

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. WebSemi-regular Decomposition Veech groups From bipartite ribbon graphs From grid graphs Outline 1 Preliminaries 2 A construction of translation surfaces From bipartite ribbon … cts boss turbo mk6Weba pair of cylinder decompositions of M, each with cylinders of com-mensurable moduli. Moreover a bound on triangle areas leads to an upper bound on certain combinatorial data associated with two cylin-der decompositions. Arguments of Thurston and Veech show that such combinatorial data determine a ﬂat surface up to aﬃne equivalence. earth with sad face clipart

"WebA cylinder decompositionof (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 will use the following well-known result to determine elements of the Veech group. It was first proven in [Vee89]for finite translation surfaces. " - Cylinder decomposition veech surface

Cylinder decomposition veech surface

VEECH SURFACES AND THEIR PERIODIC POINTS

WebAug 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-discrete set of holonomy vectors of saddle connections starting at the black point Figure 15. An angular section in which all leaves are hyperbolic Figure 16. Webcylinders of height and width (h 1,w 1) and (h 2,w 2), see Figure 1.1.4. On each cylinder we can deﬁne a Dehn twist via (x,y) 7→(x,y+µ−1xmod h), where following tradition, the …

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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 … WebAmerican Mathematical Society :: Homepage

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 ... WebJun 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 …

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.pdf

WebVEECH SURFACES AND THEIR PERIODIC POINTS 179 Theorem 1.4. Let (X,u) be an non-arithmetic Veech surface such that X is of type (g,n). For every holomorphic family of Riemann surfaces constructed from the Veech group …

Webcore(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 ... ctsb plant calibrationhttp://www-personal.umich.edu/~alexmw/Cylinder.pdf earth with satellitesWebsurface 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 ... cts brackleyWebThe 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 … earth wizard osrsWebJun 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 … ctsb proteinWebA 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 … cts both handsWebJan 1, 2006 · For a Veech surface, we give a characterization of, and an algorithm for computing, the largest possible area of ellipses symmetric with respect to the origin and … earth wizard 5e