Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 23, Issue 12, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127413300437
Keywords
Normally hyperbolic invariant manifold; bifurcation; phase space dividing surface; reaction dynamics; transition state theory
Funding
- Office of Naval Research [N00014-01-1-0769]
- Leverhulme Trust
- National Science Foundation [CHE-1223754]
- Engineering and Physical Sciences Research Council [EP/K000489/1]
- EPSRC [EP/K000489/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K000489/1] Funding Source: researchfish
- Direct For Mathematical & Physical Scien
- Division Of Chemistry [1223754] Funding Source: National Science Foundation
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In this paper, we study the breakdown of normal hyperbolicity and its consequences for reaction dynamics; in particular, the dividing surface, the flux through the dividing surface (DS), and the gap time distribution. Our approach is to study these questions using simple, two degree-of-freedom Hamiltonian models where calculations for the different geometrical and dynamical quantities can be carried out exactly. For our examples, we show that resonances within the normally hyperbolic invariant manifold may, or may not, lead to a loss of normal hyperbolicity. Moreover, we show that the onset of such resonances results in a change in topology of the dividing surface, but does not affect our ability to define a DS. The flux through the DS varies continuously with energy, even as the energy is varied in such a way that normal hyperbolicity is lost. For our examples, the gap time distributions exhibit singularities at energies corresponding to the existence of homoclinic orbits in the DS, but these singularities are not associated with loss of normal hyperbolicity.
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