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

12 votes

About positive upper density

Suppose that $(S-n)\cap S$ has upper density 0 for all $n\leq N$. Then the density of the set of integers $x$, such that $|[xN, (x+1)N]\cap S|\geq 2$ is also 0, hence the upper density of $S$ is $\leq …
Jan-Christoph Schlage-Puchta's user avatar