Helmut Rüßmann (mathematician)

Helmut Rüßmann (* 1930 ; † April 2011 in Mainz ) was a German mathematician .

Life

Helmut Rüßmann completed his mathematics studies at the Georg-August-Universität Göttingen in 1956 as a graduate mathematician. In 1958 he did his doctorate under Carl Ludwig Siegel on the existence of a normal form of true-to-content elliptical transformations . After his habilitation in 1963 at the Free University of Berlin , he worked there as a scientific adviser, professor and adjunct professor. In 1968 and 1969, Helmut Rüßmann took on a visiting professorship at Imperial College London . From 1971 until his retirement in 1999 he taught and researched as a full professor at Gutenberg University Mainz .

His field of work included ordinary differential equations and dynamic systems as well as celestial mechanics ( KAM theory ).

Publications (selection)

• About the existence of a normal form of content-faithful elliptic transformations . Göttingen, 1958 (dissertation), published in Mathematische Annalen, Volume 137, 1959, pp. 64-77 .
• On the behavior of analytical Hamiltonian differential equations in the vicinity of an equilibrium solution , Mathematische Annalen, Volume 154, 1964, pp. 285-300
• About the normal form of analytical Hamiltonian differential equations in the vicinity of the equilibrium solution , Mathematische Annalen, Volume 169, 1967, pp. 55-72
• Small denominator I: Maps of a circular ring that can be differentiated via invariant curves , Nachr. Akad. Wiss. Göttingen II Math.-Phys. Class, Volume 5, 1970, pp. 67-105
• On Optimal Estimates for the Solutions of Linear Partial Differential Equations of First Order with Constant Coefficients on the Torus , in Jürgen Moser (Hrsg.), Dynamical systems, theory and applications, 1975, Lecture Notes in Physics 38, Springer-Verlag, p. 598-624
• Convergent series developments in the perturbation theory of celestial mechanics , in Konrad Jacobs (editor), Selecta Mathematica, Volume 5, 1979, Springer Verlag (this is an introduction to the KAM theory )
• On the Existence of Invariant Curves of Twist Mappings of an Annulus , in: J. Palis (Ed.), Geometric Dynamics, 1983, Lecture Notes in Mathematics 1007, Springer-Verlag, pp. 677-718
• Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems , Regul. Chaotic Dyn., Vol. 6, 2001, pp. 119-204

Web links

• Literature by and about Helmut Rüßmann in the catalog of the German National Library

References and footnotes

1. ^ Obituary notice in the Allgemeine Zeitung Mainz . Retrieved May 1, 2011.
2. ^ Obituary: Helmut Rüßmann died at the age of 80, Johannes Gutenberg University Mainz - Johannes Gutenberg University Mainz mourns the loss of Dr. Helmut Rüßmann university professor for mathematics who died at the age of 80