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Richard McGehee

April 16, 2024

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.

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.[4][5][6]

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 edit

Selected publications edit

  • 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 edit

  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. ^ 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.
  5. ^ Saari, Donald G.; Xia, Zhihong (Jeff) (1995). "Off to infinity in finite time" (PDF). Notices of the AMS. 42 (5).
  6. ^ Alain Chenciner (2007). "The three body problem". Scholarpedia. 2 (10): 2111. Bibcode:2007SchpJ...2.2111C. doi:10.4249/scholarpedia.2111.

External links edit

  • Richard McGehee's Publication List, umn.edu

April 16, 2024
richard, mcgehee, richard, paul, mcgehee, born, september, 1943, diego, american, mathematician, works, dynamical, systems, with, special, emphasis, celestial, mechanics, mcgehee, received, from, caltech, 1964, bachelor, degree, from, university, wisconsin, ma. 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 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 4 5 6 In 1978 he was an Invited Speaker on the subject of Singularities in classical celestial mechanics at the International Congress of Mathematicians in Helsinki Contents 1 See also 2 Selected publications 3 References 4 External linksSee also editMcGehee transformationSelected publications editMcGehee 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 edit biographical information from American Men and Women of Science Thomson Gale 2004 Homepage for Richard McGehee at the U of Minnesota Richard McGehee at the Mathematics Genealogy Project 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 Saari Donald G Xia Zhihong Jeff 1995 Off to infinity in finite time PDF Notices of the AMS 42 5 Alain Chenciner 2007 The three body problem Scholarpedia 2 10 2111 Bibcode 2007SchpJ 2 2111C doi 10 4249 scholarpedia 2111 External links editRichard McGehee s Publication List umn edu Retrieved from https en wikipedia org w index php title Richard McGehee amp oldid 1171674667, wikipedia, wiki, book, books, library,

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