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math-ph2026
"Goldfish'' equations for infinitely many particles
Francois Leyvraz
The ``goldfish'' equations, so named because of their striking beauty, are a system of nonlinear ODE's, where is an arbitrary integer. They can be solved exactly in a very…
math-ph2020★ 9 cited
New algebraically solvable systems of two autonomous first-order ordinary differential equations with purely quadratic right-hand sides
F. Calogero, R. Conte, F. Leyvraz
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand…
math-ph2017
The peculiar (monic) polynomials, the zeros of which equal their coefficients
Francesco Calogero, Francois Leyvraz
We evaluate the number of monic polynomials (of arbitrary degree ) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the fo…