Veech Groups and Translation Coverings PDF Download

Author: Finster, Myriam
Publisher: KIT Scientific Publishing
ISBN: 3731501805
Category :
Languages : en
Pages : 150

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Author: Myriam Finster
Publisher:
ISBN: 9781000038927
Category :
Languages : en
Pages : 0

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Book Description
A translation surface is obtained by taking plane polygons and gluing their edges by translations. We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering. For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface. We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.

Author: J–M Gambaudo
Publisher: World Scientific
ISBN: 9814493627
Category : Science
Languages : en
Pages : 320

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Book Description
This book focuses on the interactions between discrete and geometric dynamical systems, and between dynamical systems and theoretical physics and computer science. Accordingly, the contributions revolve around two main topics: (1) interaction between geometric and symbolic systems, with emphasis on tiling problems for quasicrystals, substitutions and their multidimensional generalizations, geodesic and horocycle flow, adic systems; (2) dynamical systems: geometry and chaos, with special interest in smooth ergodic theory, statistical and multifractal properties of chaotic systems, stability and turbulence in extended complex systems. Contents: Complex Behavior in Extended System: Beyond the Lyapunov Exponent (M Cencini et al.)Generic Points via Large Deviation Theory (J T Lewis et al.)Geometry, Dynamics and Thermodynamics (H H Rugh)Iteration of Maps by Primitive Substitutive Sequences (C Holton & L Q Zamboni)Certain Partitions of a Lattice (J-I Tamura)Report on the Dynamics of Certain Piecewise Isometries of the Torus (R Adler et al.)Branched Coverings and Closed Geodesics in Flat Surfaces, with Applications to Billiards (E Gutkin)Interval Translation Mappings (J Schmeling & S Troubetkoy)and other papers Readership: Graduates and researchers in chaos and dynamical systems. Keywords:Lyapunov Exponent;Dynamics;Thermodynamics;Iteration of Maps;Lattice;Interval Translation Mappings

Author: Jayadev S. Athreya
Publisher: American Mathematical Society
ISBN: 1470476770
Category : Mathematics
Languages : en
Pages : 195

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Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.

Author: Jane Hawkins
Publisher: American Mathematical Soc.
ISBN: 1470448319
Category : Differentiable dynamical systems
Languages : en
Pages : 265

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Book Description
This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13–15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.

Author: Yunping Jiang
Publisher: American Mathematical Soc.
ISBN: 0821853406
Category : Mathematics
Languages : en
Pages : 375

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Book Description
This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Author: Carlos Matheus Silva Santos
Publisher: Springer
ISBN: 3319921592
Category : Mathematics
Languages : en
Pages : 122

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Book Description
This book is a remarkable contribution to the literature on dynamical systems and geometry. It consists of a selection of work in current research on Teichmüller dynamics, a field that has continued to develop rapidly in the past decades. After a comprehensive introduction, the author investigates the dynamics of the Teichmüller flow, presenting several self-contained chapters, each addressing a different aspect on the subject. The author includes innovative expositions, all the while solving open problems, constructing examples, and supplementing with illustrations. This book is a rare find in the field with its guidance and support for readers through the complex content of moduli spaces and Teichmüller Theory. The author is an internationally recognized expert in dynamical systems with a talent to explain topics that is rarely found in the field. He has created a text that would benefit specialists in, not only dynamical systems and geometry, but also Lie theory and number theory.

Author: André Kappes
Publisher: KIT Scientific Publishing
ISBN: 3866447515
Category : Technology & Engineering
Languages : en
Pages : 154

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Book Description
Origamis are translation surfaces obtained by gluing finitely many unit squares and provide an easy access to Teichmüller curves. In particular, their monodromy represenation can be explicitely determined. A general principle for the decomposition of this represenation is exhibited and applied to examples. Closely connected to it is a dynamical cocycle on the Teichmüller curve. It is shown that its Lyapunov exponents, otherwise inaccessible, can be computed for a subrepresentation of rank two.

Author: José María Muñoz Porras
Publisher: American Mathematical Soc.
ISBN: 0821838555
Category : Abelian groups
Languages : en
Pages : 250

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Book Description
Most of the papers in this book deal with the theory of Riemann surfaces (moduli problems, automorphisms, etc.), abelian varieties, theta functions, and modular forms. Some of the papers contain surveys on the recent results in the topics of current interest to mathematicians, whereas others contain new research results.

Author: Christian Weiß
Publisher: Springer
ISBN: 3319040758
Category : Mathematics
Languages : en
Pages : 166

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Book Description
These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmüller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.