Stability of trajectories from Poincaré to Birkhoff: approaching a qualitative definition

DOI10.1007/s00407-011-0079-0zbMath1217.01018OpenAlexW2161010517MaRDI QIDQ540717

Tatiana Roque

Publication date: 3 June 2011

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00407-011-0079-0

zbMATH Keywords

stabilitythree-body problemdifferential equationsPoincaréqualitative solutions

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematics in the 19th century (01A55) Stability theory for smooth dynamical systems (37C75)

Cites Work

• Stability by Liapunov's direct method. With applications
• Joseph Liouville's work on the figures of equilibrium of a rotating mass of fluid
• The dramatic episode of Sundman
• Oscar II's prize competition and the error in Poincaré's memoir on the three body problem
• Poincaré's discovery of homoclinic points
• The historical development of classical stability concepts: Lagrange, Poisson and Lyapunov stability
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