Dinâmica de translações em espaços projetivos

Abstract

In this work we study the dynamics of flows induced by linear transformations of finite dimension vector spaces in projective spaces, called translations. The idea is to describe the Morse components of the finest Morse decomposition of the flow, as well as the recurrent and recurrent chain sets. This is done in terms of the Jordan components of the multiplicative Jordan decomposition of the flow. Also, we study the tangent bundle to the projective space and vector subbundles to it that characterize the tangent bundle restricted to each Morse component. With this study we will demonstrate that the Morse components, of the finest Morse decomposition, are normally hyperbolic. The generalization of this result, studied about flag manifolds, is presented in the articles [5] and [20] through the language of the semisimple Lie Theory. Since projective spaces are examples of flag manifolds, the study of this work serves as an example of this theory, whose development is performed in matrix, and does not require the same arguments as the semisimple Lie Theory