### Abstract

An asymptotic and numerical study is made of the singularity structure, in the complex t-plane, of the Duffing oscillator. The presence of logarithmic terms in the local psi-series expansion, of the form t^{4} ln t, leads to a multisheeted singularity structure of great complexity. This structure is built recursively from an elemental pattern which takes the form of four-armed 'stars' of singularities. This construction is deduced analytically from the properties of the mapping z=t^{4} ln t and is confirmed quite accurately numerically. A systematic resummation of the psi series, in terms of Lame functions, is developed. This series exhibits the same analytic structure at all orders and provides a 'semi-local' analytical representation of the solution which is apparently valid even in the chaotic regime.

Original language | English (US) |
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Article number | 014 |

Pages (from-to) | 33-54 |

Number of pages | 22 |

Journal | Journal of Physics A: General Physics |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1988 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

*Journal of Physics A: General Physics*,

*21*(1), 33-54. [014]. https://doi.org/10.1088/0305-4470/21/1/014