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Chaos pp 249–290Cite as

Ordinary Differential Equations

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Abstract

Dynamical systems are often expressed in terms of ordinary differential equations. An example are the canonical equations of motion in Hamiltonian systems

$${\dot p_i} = - \frac{{\partial H}}{{\partial {q_i}}},\;{\dot p_i} = \frac{{\partial H}}{{\partial {q_i}}},$$
((12.1))

where the time derivatives of the canonical coordinates and momenta are given by the partial derivatives of the Hamiltonian. Typically, the right hand side of these equations is a nonlinear function of the variables p i and q i i.e. (12.1) is a nonlinear dynamical system.

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Authors and Affiliations

  1. Fachbereich Physik, Universität Kaiserslautern, Erwin-Schrödinger-Strasse, D-67663, Kaiserslautern, Germany

    Professor Dr. H. J. Korsch & Professor Dr. H.-J. Jodl

Authors
  1. Professor Dr. H. J. Korsch
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  2. Professor Dr. H.-J. Jodl
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© 1994 Springer-Verlag Berlin Heidelberg

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Korsch, H.J., Jodl, HJ. (1994). Ordinary Differential Equations. In: Chaos. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02991-6_12

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  • DOI: https://doi.org/10.1007/978-3-662-02991-6_12

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  • Print ISBN: 978-3-662-02993-0

  • Online ISBN: 978-3-662-02991-6

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