Cylinder decomposition veech surface

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August undefined, 2024

http://homepages.math.uic.edu/~masur/chm-rv.pdf 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 ...

Cylinder decomposition of the double pentagon surface. One cylinder …

http://www-personal.umich.edu/~alexmw/Cylinder.pdf 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. imdb my hero

Periodic points on the regular -gon

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 … WebDepartment of Mathematics The University of Chicago 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 ... imdb my christmas family tree

VEECH SURFACES AND THEIR PERIODIC POINTS

An Introduction to Veech Surfaces - ResearchGate

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 … WebSemi-regular Decomposition Veech groups From bipartite ribbon graphs From grid graphs Outline 1 Preliminaries 2 A construction of translation surfaces From bipartite ribbon … imdb my foolish heartWebVEECH 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 … imdb my life in ruins

"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 … " - Cylinder decomposition veech surface

Cylinder decomposition veech surface

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 … 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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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]. 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 …

WebJan 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 … 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.

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 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 …

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

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 imdb my small landWebsurface 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 ... imdb my accountWebSep 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 … imdb my neighbor totoro englishhttp://homepages.math.uic.edu/~masur/chm.pdf imdb my grown up christmas listWebsuch 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 … imdb mykelti williamsonWebA 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 … imdb my hero academia englishWebJun 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 … imdb my christmas inn