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Richard McGehee

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Richard Paul McGehee (born 20 September 1943 in San Diego)[1] is an American mathematician, who works on dynamical systems with special emphasis on celestial mechanics.[2]

McGehee received from Caltech in 1964 his bachelor's degree and from University of Wisconsin–Madison in 1965 his master's degree and in 1969 his Ph.D. under Charles C. Conley with thesis Homoclinic orbits in the restricted three body problem.[3] As a postdoc he was at the Courant Institute of Mathematical Sciences of New York University. In 1970 he became an assistant professor and in 1979 a full professor at the University of Minnesota in Minneapolis, where he was from 1994 to 1998 the director of the Center for the Computation and Visualization of Geometric Structures.[4] He has been at the University of Minnesota since 1970.

In the 1970s he introduced a coordinate transformation (now known as the McGehee transformation) which he used to regularize singularities arising in the Newtonian three-body problem. In 1975 he, with John N. Mather, proved that for the Newtonian collinear four-body problem there exist solutions which become unbounded in a finite time interval.[5][6][7]

In 1978 he was an Invited Speaker on the subject of Singularities in classical celestial mechanics at the International Congress of Mathematicians in Helsinki.

See also

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Selected publications

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  • McGehee, Richard (1973). "A stable manifold theorem for degenerate fixed points with applications to celestial mechanics". Journal of Differential Equations. 14 (1): 70–88. Bibcode:1973JDE....14...70M. doi:10.1016/0022-0396(73)90077-6.
  • McGehee, Richard (1974). "Triple collision in the collinear three body problem". Inventiones Mathematicae. 27 (3): 191–227. Bibcode:1974InMat..27..191M. doi:10.1007/bf01390175. S2CID 121981420.
  • with Robert A. Armstrong: McGehee, Richard; Armstrong, Robert A. (1977). "Some mathematical problems concerning the ecological principle of competitive exclusion". Journal of Differential Equations. 23 (1): 30–52. Bibcode:1977JDE....23...30M. doi:10.1016/0022-0396(77)90135-8.
  • McGehee, Richard (1981). "Double collisions for a classical particle system with nongravitational interactions". Comment. Math. Helv. 56 (1): 524–557. doi:10.1007/BF02566226. S2CID 122599392.
  • "Von Zeipel´s Theorem on singularities in celestial mechanics". Expositiones Mathematicae. 4: 335–345. 1986.
  • McGehee, Richard (1992). "Attractors for closed relations on compact Hausdorff spaces" (PDF). Indiana University Mathematics Journal. 41 (4): 1165–1209. doi:10.1512/iumj.1992.41.41058.
  • as editor with Kenneth R. Meyer: Twist mappings and their applications. Springer Verlag. 1992.

References

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  1. ^ biographical information from American Men and Women of Science, Thomson Gale 2004
  2. ^ Homepage for Richard McGehee at the U. of Minnesota
  3. ^ Richard McGehee at the Mathematics Genealogy Project
  4. ^ "Info about Richard P. McGehee". www.geom.uiuc.edu. Retrieved 2024-09-26.
  5. ^ Mather, J. N.; McGehee, R. (1975). "Solutions of the collinear four body problem which become unbounded in finite time". Dynamical Systems, Theory and Applications. Lecture Notes in Physics. Vol. 38. pp. 573–597. Bibcode:1975LNP....38..573M. doi:10.1007/3-540-07171-7_18. ISBN 978-3-540-07171-6.
  6. ^ Saari, Donald G.; Xia, Zhihong (Jeff) (1995). "Off to infinity in finite time" (PDF). Notices of the AMS. 42 (5).
  7. ^ Alain Chenciner (2007). "The three body problem". Scholarpedia. 2 (10): 2111. Bibcode:2007SchpJ...2.2111C. doi:10.4249/scholarpedia.2111.
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