The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics

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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.
Original languageEnglish
Pages (from-to)621-638
Number of pages18
JournalRegular and Chaotic Dynamics
Volume21
Issue number6
Early online date18 Dec 2016
DOIs
Publication statusE-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

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