Date | 2019-01-03 |
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Speaker | 김성찬 |

Dept. | Univ. Neuchatel |

Room | 129-104 |

Time | 10:00-11:30 |

Since Poincare the crucial role of periodic orbits in the study on dynamical systems has been known.

The restricted three-body problem has intriguing dynamics which has chaotic features. It is therefore extremely difficult to detect a periodic orbit in this problem via a direct method. It was Poincare who first looked at periodic orbits in the rotating Kepler problem, which is integrable, and followed the family they generate into the restricted three-body problem. Since periodic orbitws in integrable systems are easier to fine, Poincare's approach is very effective in the search of periodic orbits in the restricted three-body problem. In this talk we will discuss the following slightly different question: Can one decide if two periodic orbits generate the same or different families is also a difficult problem? The Cieliebak-Frauenfelder-van Koert invariants, based on the Arnold $j^+$-invariant, provide obstructions to the existence between given two periodic orbits and enable us to distinguish families. I will give a mild introduction to these invariants and present some results on the nonexistence of certain families.

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