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Mark Levi studies dynamical systems through geometry and analysis, with applications to mechanical and physical motion. His research description includes stability, geometric phases, averaging and charged-particle dynamics.

An example of the viewpoint is the inverted pendulum: a rapidly varying drive can stabilize a configuration that is unstable without it. Translating the motion into geometric or averaged descriptions can expose a simpler mechanism than direct inspection of the full trajectory.^[ref]

A researcher in dynamical stability who, with Mark Levi, analyzed a particle in a rotating saddle trap. Rapid rotation can stabilize motion even though the stationary saddle is unstable. Their calculation also finds a slow precession, represented in the averaged equations by a Coriolis-like force in the laboratory frame. This links dynamic stabilization to the behavior of a Foucault pendulum and distinguishes a rotating potential from a particle constrained to a rotating surface.^[ref]