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Local Stability

Chapter

Abstract

In this chapter we shall analyse the local topological behaviour of the orbits of vector fields. We shall show that, for vector fields belonging to an open dense subset of the space X r (M), we can describe the behaviour of the trajectories in a neighbourhood of each point of the manifold. Moreover, the local structure of the orbits does not change for small perturbations of the field. A complete classification via topological conjugacy is then provided.

Keywords

Vector Field Unstable Manifold Local Stability Stable Manifold Local Chart 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  1. 1.Instituto de Matemática Pura e AplicadaJardim BotânicoBrazil

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