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One of the well know results of Poincare state: Let f be an orientation preserving circle homeomorphism. If p/q, with mdc(p, q) = 1, is the rotation number of f, then there is a periodic point for f whose period is q. When the concept of rotations number, for orientation preserving circle homeomorphism, is generalized for torus homeomorphism f : T → T that are homotopic to the identity, it results in a convex subset of R, called rotation set and is denoted by ρ(F ) where F is a lifting of f . In the case that ρ(F ) has non-empty interior, J. Franks proved similar results to the Poincare Theorem. In this work, when ρ(F ) has empty interior, we study an similar result obtained by Jonker and Zhang. More precisely: they suppose that the rotation set ρ(F ) is a line segment with irrational slope and demonstrate that if 1 n (p1, p2) ∈ ρ(F ), with mdc(p1, p2, n) = 1, then f has a periodic point of period n.

Homeomorfismos do toro cujo conjunto de rotação é um segmento de reta