## Abstract

In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical rection dynamics. We do this by considering simple examples for one, two, and three degree-of-freedom systems where explict calculations can be carried out for all of the relevant geometrical stuctures and their properties can be explicitly understood. We specifically emphasise the notion of a NHIM as a ''phase space concept''. In particular, we make the observation that the (phase space) NHIM plays the role of ''carrying'' the (configuration space) properties of a saddle point of the potential energy surface into phase space.

We also consider an explicit example of a 2 degree-of-freedom system where a ''global'' dividing surface can be constructed using two index one saddles and one index two saddle. Such a dividing surface has arisen in several recent applications and, therefore, such a construction may be of wider interest.

We also consider an explicit example of a 2 degree-of-freedom system where a ''global'' dividing surface can be constructed using two index one saddles and one index two saddle. Such a dividing surface has arisen in several recent applications and, therefore, such a construction may be of wider interest.

Original language | English |
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Pages (from-to) | 621-638 |

Number of pages | 18 |

Journal | Regular and Chaotic Dynamics |

Volume | 21 |

Issue number | 6 |

Early online date | 18 Dec 2016 |

DOIs | |

Publication status | E-pub ahead of print - 18 Dec 2016 |

### Bibliographical note

Special issue: On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 1## Keywords

- normally hyperbolic invariant manifolds
- chemical reaction dynamics
- dividing surface
- phase space transport
- index k saddle points