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

TL;DR

This paper traces the historical development of discrete dynamics from Poincaré to May, highlighting key concepts like fixed points, chaos, and bifurcations, and emphasizing their significance in 20th-century science.

Contribution

It provides a historical overview of discrete dynamics, connecting foundational ideas to modern developments, based on a master's thesis.

Findings

Historical progression of discrete dynamics concepts

Connection between Poincaré and May's work

Emphasis on chaos and bifurcations in scientific history

Abstract

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.