Phase Portraits of Planar Vector Fields: Computer Proofs

@article{Guckenheimer1995PhasePO,
  title={Phase Portraits of Planar Vector Fields: Computer Proofs},
  author={John Guckenheimer},
  journal={Experimental Mathematics},
  year={1995},
  volume={4},
  pages={153-165}
}
Research partially supported by the National Science Foundation and the Department of Energy. We present an algorithm for computer verification of the global structure of structurally stable planar vector fields. Constructing analytical proofs for the qualitative properties of phase portraits has been difficult. We try to avoid this barrier by augmenting numerical computations of trajectories of dynamical systems with error estimates that yield rigorous proofs. Our approach lends itself to high… CONTINUE READING

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