Teorema de Pappus, Representações de Schwartz e Representações Anosov

Abstract

In the paper Pappuss Theorem and The Modular Group by Richard Schwartz [SR], the classical Pappuss theorem is seen as a dynamical system defined in an object called marked box, which is essentially a collection of points and lines in the projective plane. The dynamic ofPappus in the set of the marked boxes (CM) defines naturally a group G isomorphic to the group PSL(2, Z). Projective transformations and dualities together define the group G of projective symmetries which also acts on CM. Schwartz shows in [SR] that, given a marked box [], thereis a faithful representation : PSL(2, Z) G. Motivated by the construction of Schwartz, we define a family of Anosov representation : o G, where < 0 and o is a special subgroup of index 2 in = PSL(2, Z). When 0 then , Schwartz representation that isnot Anosov