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 Xr(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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Palis, J., de Melo, W. (1982). Local Stability. In: Geometric Theory of Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5703-5_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5703-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5705-9
Online ISBN: 978-1-4612-5703-5
eBook Packages: Springer Book Archive