Stability theory, as told by its developers

Séminaire le 5 Mai 2015, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Antonio Loria, Elena Panteley (L2S)

We present a brief but detailed historical review on the development of stability theory, from its early starts out of the minds of Lagrangia and Dirichlet. The survey carries on to focus on Lyapunov stability. Through exact citations from the works of the developers of stability, including many Soviet texts from the 20th century, we revise the fundamental definitions and theorems; making emphasis on several misfortunate translations which have led to wrong interpretations and ambiguous statements. We favour depth and sacrifice generality: on technical grounds, we focus on the most elementary (yet not so) well-known forms of Lyapunov stability and common but crucial qualifiers that go with it: uniform, asymptotic, global. We revise the origin of the wrongly known invariance principle ...