Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE ( © Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy and Legal Notice).

date: 25 February 2020

Abstract and Keywords

This article examines the role of genericity in the development of dynamical systems theory. In his memoir ‘Sur les courbes définies par une équation différentielle’, published in four parts between 1881 and 1886, Henri Poincaré studied the behavior of curves that are solutions for certain types of differential equations. He successfully classified them by focusing on singular points, described the trajectories’ behavior in important particular cases and provided new methods that proved to be extremely useful. This article begins with a discussion of singularity theory and its influence on the first definitions of genericity, along with the application of the notions of structural stability and genericity to understand dynamical systems. It also analyzes the Smale conjecture and how it was proven wrong and concludes with an overview of changes in the definitions of genericity meant to describe the ‘dark realm of dynamics’.

Keywords: genericity, dynamical systems theory, Henri Poincaré, dynamical systems, curves, differential equations, singularity theory, structural stability, Smale conjecture, trajectories

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.