Introduction to Dynamical Systems

  • Andreas Knauf
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 618)


Isaac Newton had one insight that he considered to be so fundamental that he kept it secret: “It is useful to solve differential equations.”1

The notion of dynamical systems grew out of the theory of differential equations. It was realized by Henri Poincaré that equations like the one of the celestial three body problem could not be solved analytically. Thus it was necessary to supplement the quantitative approximate solutions by qualitative methods in order to understand the long time behaviour of the solutions of differential equations.


Phase Space Riemannian Manifold Riccati Equation Unstable Manifold Haar Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Andreas Knauf
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

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