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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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A general proof for the first digit problem

Consider two sequences {$a_n$} and {$b_n$}. The former is defined as {$2^n: n = 0 \text{ to } \infty$} and the latter as { first digit (from the left) of each element in the first sequence}. The first …