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Mitchell Feigenbaum | |
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 Mitchell Feigenbaum in 2006 | |
| Born | Mitchell Jay Feigenbaum (1944-12-19)December 19, 1944 |
| Died | June 30, 2019(2019-06-30) (aged 74) New York City, New York, US |
| Citizenship | American |
| Alma mater | City College of New York(BS) Massachusetts Institute of Technology(PhD) |
| Known for | Feigenbaum constants Feigenbaum function Feigenbaum universality |
| Awards | MacArthur Fellow(1984) Wolf Prize(1986) Heineman Prize(2008) |
| Scientific career | |
| Fields | Mathematical physics |
| Institutions | Rockefeller University |
| Doctoral advisor | Francis E. Low |
Mitchell Jay Feigenbaum/ˈfaɪɡənˌbaʊm/ (December 19, 1944 – June 30, 2019) was an Americanmathematical physicist whose pioneering studies inchaos theory led to the discovery of theFeigenbaum constants.
Feigenbaum was born inPhiladelphia, Pennsylvania,[1] to Jewish emigrants fromPoland andUkraine. He attendedSamuel J. Tilden High School, inBrooklyn, New York, and theCity College of New York. In 1964, he began his graduate studies at theMassachusetts Institute of Technology (MIT). Enrolling for graduate study inelectrical engineering, he changed his area of study tophysics. He completed his doctorate in 1970 for a thesis ondispersion relations, under the supervision of ProfessorFrancis E. Low.[2]
After short positions atCornell University (1970–1972) and theVirginia Polytechnic Institute and State University (1972–1974), he was offered a longer-term post at theLos Alamos National Laboratory inNew Mexico to studyturbulence in fluids. He was at Cornell from 1982 to 1986 and then joinedRockefeller University as Toyota Professor in 1987. Although a complete theory of turbulent fluids remains elusive, Feigenbaum's research paved the way forchaos theory, providing groundbreaking insight into the many dynamical systems in which scientists and mathematicians findchaotic maps.[2]
In 1983, he was awarded aMacArthur Fellowship, and in 1986, alongside Rockefeller University colleagueAlbert Libchaber, he was awarded theWolf Prize in Physics "for his pioneering theoretical studies demonstrating the universal character of non-linear systems, which has made possible the systematic study of chaos". He was a member of the Board of Scientific Governors atthe Scripps Research Institute. He remained atRockefeller University as Toyota Professor from 1987 until his death.[2]
Some mathematical mappings involving a single linear parameter exhibit the apparently random behavior known as chaos when the parameter lies within certain ranges. As the parameter is increased towards this region, the mapping undergoesbifurcations at precise values of the parameter. At first, one stable point occurs, then bifurcates to an oscillation between two values, then bifurcating again to oscillate between four values, and so on. Feigenbaum discovered in 1975, using anHP-65 calculator, that the ratio of the difference between the values at which such successiveperiod-doubling bifurcations occur tends to a constant of around 4.6692...[3] He was able to provide a mathematical argument of that fact, and he then showed that the same behavior, with the same mathematical constant, would occur within a wide class of mathematical functions, prior to the onset of chaos.[4] This universal result enabled mathematicians to take their first steps to unraveling the apparently intractable "random" behavior of chaotic systems. The "ratio of convergence" measured in this study is now known as the firstFeigenbaum constant.[2]
Thelogistic map is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: "Quantitative Universality for a Class of Nonlinear Transformations".[5]
Feigenbaum's other contributions include the development of important newfractal methods incartography, starting when he was hired by Hammond to develop techniques to allow computers to assist in drawing maps. The introduction to theHammond Atlas (1992) states:
Usingfractal geometry to describe natural forms such as coastlines, mathematical physicist Mitchell Feigenbaum developed software capable of reconfiguring coastlines, borders, and mountain ranges to fit a multitude of map scales and projections. Dr. Feigenbaum also created a new computerized type-placement program which places thousands of map labels in minutes, a task that previously required days of tedious labor.[6]
In another practical application of his work, he foundedNumerix withMichael Goodkin in 1996. The company's initial product was a software algorithm that dramatically reduced the time required forMonte Carlo pricing of exoticfinancial derivatives andstructured products.
The press release made on the occasion of his receiving theWolf Prize summed up his works:
The impact of Feigenbaum's discoveries has been phenomenal. It has spanned new fields of theoretical and experimental mathematics ... It is hard to think of any other development in recent theoretical science that has had so broad an impact over so wide a range of fields, spanning both the very pure and the very applied.[2]
A semipopular account of the universal scaling theory for the period doubling route to chaos is presented.
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