The mathematician Hugo Ribeiro.
Aristotle and even earlier scientist and philosophers attempted to define, or at least to through light upon randomness. The author sketches the attempts to direct concept of randomness into the realm of mathematical science from Aristotle up to Poincaré. He dwells on the various interpretations of randomness that were pronounced in natural science and philosophy, and on the interrelation between necessity and randomness.
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.
The Poincaré-Bendixson Theorem and the development of the theory are presented - from the papers of Poincaré and Bendixson to modern results.