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Microcanonical rates, gap times, and phase space dividing surfaces
1.R. Marcelin, Ann. Phys. (Paris) 3, 120 (1915).
5.O. K. Rice, Z. Phys. Chem. 7, 226 (1930).
8.L. S. Kassel, The Kinetics of Homogenous Gas Reactions (Chemical Catalog, New York, 1932).
9.C. N. Hinshelwood, The Kinetics of Chemical Change (Clarendon, Oxford, 1940).
10.N. B. Slater, Theory of Unimolecular Reactions (Cornell University Press, Ithaca, 1959).
11.D. L. Bunker, Theory of Elementary Gas Reaction Rates (Pergamon, Oxford, 1966).
12.H. S. Johnston, Gas Phase Reaction Rate Theory (Ronald, New York, 1966).
13.O. K. Rice, Statistical Mechanics, Thermodynamics, and Kinetics (W. H. Freeman, San Francisco, 1967).
14.K. J. Laidler, Theories of Chemical Reaction Rates (McGraw-Hill, New York, 1969).
15.P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (Wiley, New York, 1972).
16.W. Forst, Theory of Unimolecular Reactions (Academic, New York, 1973).
17.E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes (Clarendon, Oxford, 1974).
18.I. W. M. Smith, Kinetics and Dynamics of Elementary Gas Reactions (Butterworths, London, 1980).
19.J. H. Beynon and J. R. Gilbert, Application of Transition State Theory to Unimolecular Reactions: An Introduction (Wiley, New York, 1984).
20.H. O. Pritchard, The Quantum Theory of Unimolecular Reactions (Cambridge University Press, Cambridge, 1984).
22.R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions (Blackwell Scientific, Oxford, 1990).
23.T. Baer and W. L. Hase, Unimolecular Reaction Dynamics (Oxford University Press, New York, 1996).
25.W. Forst, Unimolecular Reactions (Cambridge University Press, Cambridge, 2003).
26.Unimolecular Kinetics: Part 1. The Reaction Step, Comprehensive Chemical Kinetics, Vol. 39, edited by N. J. B. Greene (Elsevier, New York, 2003).
27.M. Zhao, J. Gong, and S. A. Rice, Adv. Chem. Phys. 130A, 3 (2005).
28.N. E. Henriksen and F. Y. Hansen, Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics (Oxford University Press, New York, 2008).
30.U. Lourderaj and W. L. Hase, J. Phys. Chem. A (unpublished).
38.W. L. Hase, in Modern Theoretical Chemistry, edited by W. H. Miller (Plenum, New York, 1976), Vol. 2, pp. 121–170.
48.S. Y. Grebenshchikov, R. Schinke, and W. L. Hase, in Unimolecular Kinetics: Part 1. The Reaction Step, Comprehensive Chemical Kinetics, Vol. 39, edited by N. J. B. Greene (Elsevier, New York, 2003), pp. 105–242.
67.E. Thiele, M. F. Goodman, and J. Stone, Opt. Eng. 19, 10 (1980).
76.J. Mikosch, S. Trippel, C. Eichhorn, R. Otto, U. Lourderaj, J. X. Zhang, W. L. Hase, M. Weidemuller, and R. Wester, Science 319, 183 (2008).
85.R. S. MacKay and J. D. Meiss, Hamiltonian Dynamical Systems: A Reprint Selection (Taylor & Francis, London, 1987).
86.A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer Verlag, New York, 1992).
87.S. Wiggins, Chaotic Transport in Dynamical Systems (Springer-Verlag, New York, 1992).
88.V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics (Springer, New York, 2006).
90.P. Pechukas, Ber. Bunsenges. Phys. Chem. 86, 372 (1982).
91.E. Pollak, Periodic Orbits and the Theory of Reactive Scattering, Theory of Chemical Reaction Dynamics, Vol. 3 (CRC, Boca Raton, 1985), pp. 123–246.
96.D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987).
99.M. J. Davis and R. T. Skodje, Chemical Reactions as Problems in Nonlinear Dynamics, Advances in Classical Trajectory Methods, Vol. 3 (JAI, Greenwich, 1992), pp. 77–164.
115.S. H. Tersigni and S. A. Rice, Phys. Chem. Chem. Phys. 92, 227 (1988).
123.V. I. Arnold, Sov. Math. Dokl. 5, 581 (1964).
124.P. Lochak, in Hamiltonian Systems with Three or More Degrees of Freedom, edited by C. Simo (Kluwer, Dordrecht, 1999), pp. 168–183.
141.G. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, New York, 2005).
145.S. Wiggins, Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Springer-Verlag, New York, 1994).
147.The codimension of a submanifold is the dimension of the space in which the submanifold exists, minus the dimension of the submanifold. The significance of a submanifold being “codimension one” is that it is one less dimension than the space in which it exists. Therefore it can “divide” the space and act as a separatrix, or barrier, to transport.
180.D. J. Wales, Energy Landscapes (Cambridge University Press, Cambridge, 2003).
181.P. G. Mezey, Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).
182.Such a separation is assumed to be meaningful for the range of energies considered here.
183.V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics, Vol. 60 (Springer, New York, 1978).
184.J. Binney, O. E. Gerhard, and P. Hut, Mon. Not. R. Astron. Soc. 215, 59 (1985).
193.The quantity is therefore the effective value for the fraction of trapped states as determined on the time scale of the calculation. The true behavior of the survival probability at extremely long times has not however been fully characterized, and merits further study.
196.The recent work of Paskauskas et al. (Refs. 194 and 195) has advanced our understanding of the trapping problem in three DoF systems. One-parameter families of singly resonant 2-tori in the vicinity of elliptically stable periodic orbits are identified as the “backbone” of the resonance zone associated with such periodic orbits. According to this picture, trapped trajectories initiated close to a stable periodic orbit move in the vicinity of the resonant 2-tori until they reach a sufficiently unstable (normally hyperbolic) 2-torus, at which point they pass along the unstable manifolds of the 2-tori and escape to another region of phase space.
197.J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1983).
199.E. Ott, Chaos in Dynamical Systems, 2nd ed. (Cambridge University Press, Cambridge, 2002).
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