This article is cited in 12 papers

Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature

E. A. Gutkin^ab, S. L. Tabachnikov<sup>c

a</sup> Instituto Nacional de Matemática Pura e Aplicada
^b University of California, Los Angeles
^c Department of Mathematics, Pennsylvania State University

Abstract: 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.

Key words and phrases: Geodesic polygon, constant curvature, complexity, inner billiard, outer billiard.

MSC: 53D25, 37E99, 37B10

Received: April 29, 2006; in revised form October 16, 2006

Language: English

DOI: 10.17323/1609-4514-2006-6-4-673-701

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