Ergodicity of polygonal slap maps

Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflections laws. We study the absolutely continuous invariant probabilities of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps having more than one ergodic absolutely continuous invariant probability.Comment: 17 pages, 6 figure

Hyperbolic polygonal billiards with finitely many ergodic SRB measures

We study polygonal billiards with reflection laws contracting the reflected angle towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic SRB measures whose basins cover a set of full Lebesgue measure.Comment: 26 pages, 2 figure

Sistema Integrado de Gestão em Indústria de Insumos Farmacêuticos

A implementação de um Sistema Integrado de Gestão (SIG) para a Indústria de Insumo Farmacêutico, certificada com as Boas Práticas de Fabricação (BPF), usando como diretrizes as normas NBR ISO 9001:2000, NBR ISO 14001:2004, NBR 16001:2004 e OHSAS 18001:2007, pode ser implantado através de etapa