Mathematical Sciences: Transport and Long Time Stability Dynamical Systems

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9505017 Dumas The proposed research is in the area of dynamical systems; in particular, averaging and stability of Hamiltonian systems are to be investigated. The investigator proposes to generalize Anosov's averaging theorem to systems with more general hypotheses on the driving flow; proposes to apply Lasker's frequency analysis to the study of transport in symplectic maps. Hamiltonian systems arise in celestial mechanics, accelerator physics and elsewhere in nature. The frequency analysis method, first developed by Lasker, can be applied to a variety of such systems to detect long time instability. The proposed research seeks to provide a rigorous theoretical framework for this method.