Infinite Genus Surfaces and Irrational Polygonal Billiards

نویسنده

  • FERRÁN VALDEZ
چکیده

We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus real topological surface with exactly one end.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Veech Groups, Irrational Billiards and Stable Abelian Differentials

We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we prove that these groups are non-discrete subgroups of SO(2,R) and we calculate their rank.

متن کامل

Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards

ABSTRACT We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.

متن کامل

ha o - dy n / 99 03 03 2 v 1 2 3 M ar 1 99 9 On the classical dynamics of billiards on the sphere

We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature cases we obtain a complex but regular dynamics.

متن کامل

Billiards and Teichmüller curves on Hilbert modular surfaces

This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

متن کامل

Complexity of Piecewise Convex Transformations in Two Dimensions, with Applications to Polygonal Billiards on Surfaces of Constant Curvature

We introduce piecewise convex transformations, and develop geometric tools to study their complexity. We apply the results to the complexity of polygonal inner and outer billiards on surfaces of constant curvature. 2000 Math. Subj. Class. 53D25, 37E99, 37B10.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009