Mathematical Sciences: Hamiltonian Dynamics

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9627979 Gole This project uses variational techniques to prove the existence of orbits of many different topological types in conservative dynamical systems. In addition, the investigator will consider the method of frequency analysis introduced by J. Lasker and apply them to detect chaos and diffusion in conservative systems. One of the proposed goals is to give a firm mathematical foundation of Lasker's method, which at present is mostly a numerical method. Chaos and diffusion phenomena in dynamical systems have wide ranging applications in the physical world. For example, they can be used to model certain weather systems involving turbulence and sudden bifurcation.