Journée de Dynamique Non Linéaire

10h30   Turgay Uzer (Georgia Institute of Technology)
Transition states in phase space: from atoms to planets

11h35   Elena Shchekinova (Georgia Institute of Technology)
Phase Space Structures of OCS Molecule using Frequency Analysis and Fast Lyapunov Indicator

Résumé du séminaire de Elena Shchekinova

The dynamics of the planar OCS molecule which is a Hamiltonian system with three degrees of freedom is known to be strongly chaotic for energies close to the dissociation threshold. The planar and collinear models of the OCS molecule have been studied extensively by C. C. Martens et al. [Chem. Phys. Lett. 142, 519 (1987)]. They have applied local frequency analysis by using Fast Fourier Transform to study phase space structures and to analyze the main resonances. Long-time correlations were observed for the planar OCS model, and a mechanism for chaotic transport in the system was proposed. In our work we use the numerical frequency analysis method developed by J. Laskar. It allows one to give a much more accurate approximation of the main frequencies of the system. We locate regular and chaotic zones for the phase space of OCS by computing the frequency map, and identify the existing resonances. The use of Laskar's frequency analysis method for the OCS molecule requires a lot of computational time. The novel method of fast Lyapunov indicators gives very fast and accurate prediction of the stability of orbits. We can easily discriminate resonant, nonresonant, and chaotic regions in phase space for the OCS molecule by computing the Lyapunov field.