Every ordinary differential equation with a strict Lyapunov function is a gradient system

Tomáš Bárta (1) , Ralph Chill (2) , Eva Fašangová (1)

1 UK - Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic]
2 LMAM - Laboratoire de Mathématiques et Applications de Metz

We explain and prove the statement from the title. This allows us to formulate a new type of gradient inequality and to obtain a new stabilization result for gradient-like ordinary differential equations.

Mots clés: Kurdyka-Lojasiewicz gradient inequality; gradient system; Strict Lyapunov function; convergence to equilibrium; damped second order ordinary differential equation

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]; Systèmes dynamiques [math.DS]

Tomáš Bárta, Ralph Chill, Eva Fašangová. Every ordinary differential equation with a strict Lyapunov function is a gradient system. Monatshefte für Mathematik, 2012, 166 (1), pp.57-72. ⟨10.1007/s00605-011-0322-4⟩. ⟨hal-01275665⟩