Cylinder decomposition veech surface

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August undefined, 2024

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 … 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

A cylinder decomposition for the regular octagon surface

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. http://homepages.math.uic.edu/~masur/chm-rv.pdf how much is goofy\u0027s kitchen

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Webexamine how these segments intersect di erent sets of cylinders and use at surface techniques to deduce which points on these lines are periodic. The regular n-gon and … 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. 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 … how do emotions affect sports performance

The GL(2,R) Action, the Veech Group, Delaunay Decomposition

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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. WebThe proofs combine recent results on Masur–Veech volumes of moduli spaces of meromorphic quadratic differentials in genus zero with our new observation that horizontal and vertical separatrix diagrams of integer quadratic … how much is goodyear worthWebbecause 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. how much is google analytics premium

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Cylinder decomposition veech surface

Dilation surfaces and their Veech groups - aimsciences.org

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 ... 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.

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WebDec 19, 2016 · 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 … 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].

Websurface 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 ... 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 Veech surface (X,q) is called primitive if it cannot be realized as a branched cover over (X′,q′), where the genus of X′ is lower than the genus of X and the quadratic diﬀerential q′ pulls back to q under the covering map. If (X,q) is a Veech surface that is not primitive, then the corresponding surface (X′,q′) is also Veech WebMore precisely, regular n-gon surfaces have (n, ∞, ∞)-triangle groups as Veech groups, while the Veech groups of Bouw-Möller surfaces are (m, n, ∞)-triangle groups for m and n not both even ...

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 …

WebA 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 … how do embroidery sewing machines workWebJun 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 … how much is google 1 membershipWebSurface Area of Cylinder. The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the surface area of the cylinder is equal to the total surface area of the … how do emotions behave as motivatorsWebSep 26, 2024 · The volume of the cylinder is referred to as the density or amount of space it occupies. We have, Volume of a cylinder = Area of a circle × height. Since, we have an … how do emotions affect usWebAug 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 … how do emotions directly affect usWebMay 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 … how much is google assistantWebVEECH 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 … how much is goodyear tire