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Let X be a hyperbolic linear vector field on IR", with index n (or O), U be an open set in IR" containing the origin and f: U —) IR" a Cr-diffeomorphism, r > 1, such that f maps orbits of X in U to orbits of X in IR" and preserves Uo the orientation. Denote U0 = U — {O} and let — be the differentiable manifold X obtained by identifying each orbit of X In U to a point. In this work we study the vo map induced by f, J: 7 We also study with more detail the case n = 2. This dissertation is based on the paper [1] by C. Camacho and A. Lins Neto.

Difeomorfismos que Preservam Órbitas de Campos de Vetores Lineares Hiperbólicos