- Eberhard Hopf
Eberhard Frederich Ferdinand Hopf (
April 4 ,1902 Salzburg, Austria –July 24 ,1983 Bloomington, Indiana) was amathematician andastronomer , one of the founding fathers ofergodic theory and a pioneer ofbifurcation theory who also made significant contributions to the subjects ofpartial differential equation s andintegral equation s,fluid dynamics , anddifferential geometry . TheHopf maximum principle is an early result of his (1927) which is one of the most important techniques in the theory ofelliptic partial differential equation s.Biography
Eberhard Hopf was born in
Salzburg ,Austria , but his scientific career was divided betweenGermany and theUnited States . He received his Ph.D. in Mathematics in 1926 and hisHabilitation in Mathematical Astronomy from the University of Berlin in 1929.In 1930 he received a fellowship from the
Rockefeller Foundation to studyclassical mechanics with George Birkhoff atHarvard , but his appointment was at the Harvard College Observatory. In late 1931, with the help ofNorbert Wiener , Hopf joined the Department of Mathematics of theMassachusetts Institute of Technology , accepting the position of Assistant Professor. While at MIT, Hopf did much of his work onergodic theory .In Cambridge Hopf worked on many mathematical and astronomical subjects. His paper "On time average theorem in dynamics", which appeared in the
Proceedings of the National Academy of Sciences , is considered by many to be the first readable paper in modern ergodic theory. His book "Mathematical problems of radiative equilibrium" first appeared in 1934 and was reprinted in 1964. Another important contribution from this period is the theory ofWiener-Hopf equation s, which he developed in collaboration with Norbert Wiener. By 1960, a discrete version of these equations was being extensively used in electrical engineering and geophysics, their use continuing until the present day. During this time, Hopf gained a reputation for his ability of illuminating the most complex subjects for his colleagues and even for non-specialists. Because of this talent, many discoveries and proofs of other mathematicians became easier to understand after they had been described by Hopf. In 1936 Hopf received and accepted an offer of a full professorship from theUniversity of Leipzig . Hopf, with his wife Ilse and their infant daughter Barbara, returned to Germany, which by this time was under the control of theNazi Party .The book "Ergodentheorie", most of which was written when Hopf was still at the Massachusetts Institute of Technology, was published in 1937. In that book, containing only 81 pages, Hopf presented a precise and elegant summary of ergodic theory. In 1939 Hopf established ergodicity of the
geodesic flow oncompact manifolds of constant negative curvature. In 1940 Hopf was on the list of the invited lecturers to theInternational Congress of Mathematicians to be held inCambridge, Massachusetts . Because of the start ofWorld War II , however, the Congress was cancelled.In 1942 Hopf was drafted to work in the German Aeronautical Institute. In 1944, one year before the end of World War II, Hopf was appointed to a professorship at the
University of Munich . In 1947, at the behest ofRichard Courant he returned to the United States, where he presented the definitive solution of Hurewicz's problem.Fact|date=February 2008On 22 February 1949 Hopf became a US citizen and joined Indiana University at Bloomington as a Professor of Mathematics. In 1962 he was made Research Professor of Mathematics, staying in that position until his death.
Hopf was never forgiven by many people for his moving to Germany in 1936, where the Nazi party was in power. As a result, most of his work in ergodic theory and topology was neglected or even attributed to others in the years following the end of World War II. An example of this was the expulsion of Hopf's name from the discrete version of the Wiener–Hopf equations, which were frequently referred to as "
Wiener filter ".Awards and honors
In 1971 Hopf was the American Mathematical Society Gibbs Lecturer.
ee also
*
Hopf alternative
*Hopf bifurcation
*Hopf–Cole transformation (seeBurgers' equation )
*Wiener–Hopf method Bibliography
* "Selected works of Eberhard Hopf with commentaries". Edited by Cathleen S. Morawetz, James B. Serrin and Yakov G. Sinai.
American Mathematical Society , Providence, RI, 2002. xxiv+386 pp ISBN 0-8218-2077-X MathSciNet|id=1985954External links
*MacTutor Biography|id=Hopf_Eberhard
*MathGenealogy|id=12959Persondata
NAME= Hopf, Eberhard
ALTERNATIVE NAMES=
SHORT DESCRIPTION=Austrian mathematician
DATE OF BIRTH=April 4 ,1902
PLACE OF BIRTH=Salzburg, Austria
DATE OF DEATH=July 24 ,1983
PLACE OF DEATH=Indianapolis ,Indiana
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