Extending Ordinary Differential Equations to Metric Spaces: Aubin’s Suggestion

Abstract

This chapter is devoted to Aubin)s original concept of mutational equations introduced in the early 1990s. They provide an interesting extension of ordinary differential equations to a metric space (instead of the classical Euclidean space ℝ^N). The main challenge to which Aubin suggested an interesting answer is how to dispense with any linear structure of the basic set while following the popular track of ordinary differential equations up to solutions to the initial value problem.