### Abstract

We applied the method of the short time Lyapunov indicators to the planar circular and to the planar elliptic restricted three-body problem in order to study the structure of the phase space in some selected regions. In the circular case we computed the short-time averages of the stretching numbers to distinguish between regular and chaotic domains of the phase space. The results obtained in this way are in good agreement with the corresponding Poincaré's surface of sections. Using the short time Lyapunov indicators we determined the detailed structure of the phase space in the semimajor axis-eccentricity plane of the test particle both in the circular and in the elliptic restricted problem (in the latter case for some values of the eccentricities of the primaries) and we studied the main features of the phase space.

Original language | English |
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Pages (from-to) | 29-40 |

Number of pages | 12 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 79 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2001 |

### Keywords

- Poincaré's surface of section
- Restricted three-body problem
- Short time lyapunov indicators
- Stretching numbers

### ASJC Scopus subject areas

- Modelling and Simulation
- Mathematical Physics
- Astronomy and Astrophysics
- Space and Planetary Science
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Celestial Mechanics and Dynamical Astronomy*,

*79*(1), 29-40. https://doi.org/10.1023/A:1011113928311