Scattering theory is a convenient way to describe systems that are subject to time-dependent perturbations which are localized in time. Using scattering theory, one can compute time-dependent invariant objects for the perturbed system knowing the invariant objects of the unperturbed system. In this paper, we use scattering theory to give numerical computations of invariant manifolds appearing in laser-driven reactions. In this setting, invariant manifolds separate regions of phase space that lead to different outcomes of the reaction and can be used to compute reaction rates. V C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767656] In this paper, we implement numerically the theoretical ideas of Blazevski and de la Llave (2011) using the laser-driven H enon-Heiles system introduced in Kawai et al. (2007). The ideas of this paper are robust and can be used for any system subject to a time-dependent perturbation localized in time. Using the intertwining relations, scattering theory yields a time-dependent conjugacy between the perturbed and unperturbed systems. Assuming one has the relevant invariant manifolds for the unperturbed system, we exploit the conjugacy to compute the corresponding objects for the perturbed system. The algorithm used in this paper to compute invariant manifolds is an alternative to the use of time-dependent normal form theory used in Kawai et al. (2007) and is readily parallelizable.

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Abstract.We consider the complete hyperelliptic integral Using a recent result concerning the Taylor expansion of the 6-Dirac function, we write J(a) as a power series of a parameter involving a and the Ajt's.We prove this series to be a sum of multiple hypergeometric series which reduces to a single term when the number of odd monomial terms in Pn is less than or equal to one. The region of convergence is then studied and a few particular cases are detailed.

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