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

18 votes
1 answer
483 views

Iterated antiderivatives of polynomials having many real roots

Question For which polynomials $p_n:\mathbb{R} \rightarrow \mathbb{R}$ having $n$ distinct real roots can we find an infinite sequence of polynomials $$ p_n, p_{n+1}, p_{n+2} , p_{n+3}, \dots, $$ suc …