The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Lyapunov Functions

  • C. Henry
Reference work entry


Within twelve years, from Poincaré’s Mémoire sur les courbes définies par une équation différentielle (1881–1886) to Lyapunov’s thesis Obshcˇaya zadacˇa ob unstoicˇivosti dvizˇeniya (1892), the qualitative theory of differential equations emerged almost from scratch as the core of a new field in mathematics; both Poincaré and Lyapunov were motivated by problems in mechanics, celestial mechanics above all. Even if he did not match Poincaré’s prodigious creativity between 1880 and 1883, Lyapunov developed from 1888 to 1892 a theory of dynamical stability which makes his 1892 thesis both a pioneering piece of work and a classic; in particular he developed a general stability criterion which now bears his name: the Lyapunov function.

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • C. Henry
    • 1
  1. 1.