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This article is cited in 45 scientific papers (total in 45 papers)
The Role of Normally Hyperbolic Invariant Manifolds (NHIMs) in the Context of the Phase Space Setting for Chemical Reaction Dynamics
Stephen Wiggins School of Mathematics, University of Bristol,
Bristol, BS8 1TW, United Kingdom
Abstract:
In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical reaction dynamics. We do this by considering simple examples for one-, two-, and three-degree-of-freedom systems where explicit calculations can be carried out for all of the relevant geometrical structures and their properties can be explicitly understood. We specifically emphasize 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.
Keywords:
normally hyperbolic invariant manifolds, chemical reaction dynamics, dividing surface, phase space transport, index $k$ saddle points.
Received: 12.10.2016 Accepted: 04.11.2016
Citation:
Stephen Wiggins, “The Role of Normally Hyperbolic Invariant Manifolds (NHIMs) in the Context of the Phase Space Setting for Chemical Reaction Dynamics”, Regul. Chaotic Dyn., 21:6 (2016), 621–638
Linking options:
https://www.mathnet.ru/eng/rcd213 https://www.mathnet.ru/eng/rcd/v21/i6/p621
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Abstract page: | 292 | References: | 34 |
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