Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Numerical study of quadratic area-preserving mappings


Author: M. Hénon
Journal: Quart. Appl. Math. 27 (1969), 291-312
MSC: Primary 65.10
DOI: https://doi.org/10.1090/qam/253513
MathSciNet review: 253513
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Abstract: Dynamical systems with two degrees of freedom can be reduced to the study of an area-preserving mapping. We consider here, as a model problem, the mapping given by the quadratic equations: $ {x_1} = x\cos \alpha - \left( {y - {x^2}} \right)\sin \alpha $, $ {y_1} = x\sin \alpha + \left( {y - {x^2}} \right) \\ \cos \alpha $, which is shown to be in a sense the simplest nontrivial mapping. Some analytical properties are given, and numerical results are exhibited in Figs. 2 to 14.


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DOI: https://doi.org/10.1090/qam/253513
Article copyright: © Copyright 1969 American Mathematical Society


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