Introduction and Statement of the Main Results

Abstract

Nowadays most scientific research is written in the language of ordinary differential equations (ODEs). Since the times these equations appeared first in the works of G.W. Leibnitz (1646–1716) and I. Newton (1642–1727), more and more fields of knowledge found and continue to find in them an accurate language to determine and to develop their knowledge. Astronomy, and in particular Celestial Mechanics, Physics and Chemistry found in differential equations the most natural way of expressing their laws. Engineering, Economics, Ecology, Epidemiology, Neuroscience, etc., use this language in order to model natural phenomena and to simulate their behaviour in theoretical and numerical experiments that hardly could be carried out in a laboratory. As a result, the study of ODEs became one of the areas of mathematics with a very large number of applications.