Generic one-parameter families of vector fields on two-dimensional manifolds

@article{Sotomayor1974GenericOF,
  title={Generic one-parameter families of vector fields on two-dimensional manifolds},
  author={Jorge Sotomayor},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  year={1974},
  volume={43},
  pages={5-46}
}
  • J. Sotomayor
  • Published 1 December 1974
  • Mathematics
  • Publications Mathématiques de l'Institut des Hautes Études Scientifiques
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References

SHOWING 1-10 OF 11 REFERENCES
Differentiable dynamical systems
This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a
The Closing Lemma
Introduction to Differentiable Manifolds
Foreword.- Acknowledgments.- Differential Calculus.- Manifolds.- Vector Bundles.- Vector Fields and Differential Equations.- Operations on Vector Fields and Differential Forms.- The Theorem of
Ordinary Differential Equations
Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential
On Structural Stability
Theory of Ordinary Differential Equations
The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably
...
1
2
...