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

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Continuity of the period for a periodic dynamical system

The answer is trivially negative already for $n=3$: Start with the flow following along the "long" lines of a thickened (say with disc-shaped cut) Möbius strip. You can imagine this like a thick “rope …
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