From Poincar\'e to May: The Genesis of Discrete Dynamics

In this paper, the origin of discrete dynamics is stated from a historical point of view, as well as its main ideas: fixed and periodic points, chaotic behaviour, bifurcations. This travel will begin with Poincar'e’s work and will finish with May’s work, one of the most important scientific papers of 20th century. This paper is based on the M.Sc. thesis “Simple Permutations, Pasting and Reversing”, written by the first author under the guidance of the second author.