From Abel equations to Jacobian conjecture

International audienceThis is a survey relating several subjects bridging algebraic differential equations and their integrability, pertubative approach based on algebraic moments, the Jacobian conjecture and optimal transport of measures defined on the complement of an arrangement of hyperplanes. This text was written in relation with Jaume Llibre's 60th birthday and it touches several fields in which Jaume gave important contributions. It also contains some results wich have not yet been published before