Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards
نویسنده
چکیده
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.
منابع مشابه
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 کاملOn the Bernoulli property of planar hyperbolic billiards
We consider billiards in bounded non-polygonal domains of R with piecewise smooth boundary. More precisely, we assume that the curves forming the boundary are straight lines or strictly convex inward curves (dispersing) or strictly convex outward curves of a special type (absolutely focusing). It follows from the work of Sinai, Bunimovich, Wojtkowski, Markarian and Donnay [S, Bu2, W2, M1, Do, B...
متن کاملPeriodicity of certain piecewise affine planar maps
In the past few decades, discontinuous piecewise affine maps have found considerable interest in the theory of dynamical systems. For an overview, we refer the reader to [1, 7, 12, 13, 17, 18], for particular instances to [29, 16, 25] (polygonal dual billiards), [15] (polygonal exchange transformations), [10, 31, 11, 8] (digital filters) and [19, 21, 22] (propagation of round-off errors in line...
متن کاملOn Polygonal Dual Billiard in the Hyperbolic Plane
Given a compact convex plane domain P , one defines the dual billiard transformation F of its exterior as follows. Let x be a point outside of P . There are two support lines to P through x; choose one of them, say, the right one from x’s view-point, and define F (x) to be the reflection of x in the support point. This definition applies if the support point is unique; otherwise F (x) is not de...
متن کاملPolygonal Approximation of Voronoi Diagrams of a Set of Triangles in Three Dimensions
We describe a robust adaptive marching tetrahedra type algorithm for constructing a polygonal approximation of the Voronoi Diagram of an arbitrary set of triangles in three dimensions. Space is adaptively subdivided into a set of tetrahedral cells, and the set of Voronoi regions which intersect each cell is determined exactly using a simple primitive we introduce. We obtain a small number of di...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005