Jürgen Moser
The third initial of KAM, who proved that Kolmogorov's theorem survives when the Hamiltonian is merely smooth rather than analytic.
Biography
Jürgen Moser was born in Königsberg in 1928. He studied in Göttingen under Franz Rellich and Carl Ludwig Siegel, the last great custodian of nineteenth-century celestial mechanics, and emigrated to the United States in 1955, eventually taking a long professorship at the Courant Institute in New York.
In 1962, working independently of Kolmogorov and Arnold and with a rather different technique — a convergent-iteration scheme now called the Nash-Moser theorem — he proved the invariant-torus result for smooth Hamiltonians, where analyticity cannot be assumed. The three proofs together are the KAM theorem. Moser spent the rest of his career at ETH Zurich, where he directed the Mathematical Research Institute and trained a generation of analysts on the continent.
His interests ranged from celestial mechanics to minimal surfaces to integrable systems to the geometry of partial differential equations. He was known for a style that was quiet, precise, and devastatingly direct: colleagues recalled that a 'Moser lecture' was shorter than other lectures and twice as clear. He died in Zurich in 1999.
Contributions
- 01Proved the smooth case of the KAM theorem (1962)
- 02Developed the Nash-Moser implicit function theorem for nonlinear PDE
- 03Co-authored Lectures on Celestial Mechanics with Siegel
- 04Moser's twist theorem on area-preserving maps of the annulus