Symplectic Camels and Uncertainty Analysis
نویسنده
چکیده
Gromov’s non-squeezing theorem is a relatively new results in symplectic topology that provides a non-trivial constraint on the propagation of uncertainty in a Hamiltonian system. While the application to nonlinear systems is difficult, one can apply the theorem to obtain bounds on the propagation of uncertainty in the linearized system, by exploiting the fact that the flow of the linearization of a Hamiltionian system is still symplectic. This report compares the results that one obtains by this linearized analysis to the actual behavior of the nonlinear system.
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