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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

3 votes

Necessary and sufficient curvature condition for a regular planar curve to be simple and closed

The Four-vertex theorem dictates that the curvature function needs to have at least two local minima and maxima. The converse of the four-vertex theorem tells us that there's at least one parametrizat …
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