We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in the plane that contains the circle. The study presented here is purely analytic.

We show the existence of periodic solutions for continuous symmetric perturbations of certain planar power law problems.In this paper we study continuous symmetric perturbations of planar power law problems of the form. In particular, if = 1, the unperturbed problem is Kepler's problem.We prove the existence of periodic solutions of perturbed problems as above, close to a given circular orbit of the unperturbed problem. We have two cases. When = 1 (that is, the unperturbed problem is Kepler's problem) we will require that the perturbed problems are symmetric with respect to the x and y axes. For = 1, we will require just one symmetry.

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.

This work intends to present the mechanisms used by the "development" and the experiences of the people compulsorily displaced due to the Irapé HPP in the Jequitinhonha Valley, stigmatized as a "valley of misery". For this purpose, literature review, qualitative research, case study, field work, etc. It was carried in October Also Analyzes the Disproportionate power to suppress rights and lead the population to accept the "rules of the game". The pressures for homogenization que Suppresses the socio -cultural diversities of the "being and doing" of the peasant, the emptying and disqualification of the c onfrontations that make invisible the social movements. The relativization of the symbolic value of land, inheritance, traditions, way of life and the multiple uses of land and nature, Which are despised by entrepreneurs. In this way, the resolution of con flicts is enabled by reification, Which Merely prioritizes the economic logic, Which Understands the people of the place object to another in the natural landscape.