Bulletin of the American Mathematical Society

George David Birkhoff and his mathematical work

Marston Morse

Article information

Source
Bull. Amer. Math. Soc., Volume 52Number 5, Part 1 (1946), 357-391.

Dates
First available in Project Euclid: 4 July 2007

https://projecteuclid.org/euclid.bams/1183507914

Mathematical Reviews number (MathSciNet)
MR0016341

Zentralblatt MATH identifier
0060.01409

Citation

Morse, Marston. George David Birkhoff and his mathematical work. Bull. Amer. Math. Soc. 52 (1946), 357--391. https://projecteuclid.org/euclid.bams/1183507914

References

• 1. George David Birkhoff, with H. S. Vandiver, On the integral divisors of $a^n b^n$, Ann. of Math. vol. 5 (1904) pp. 173-180.
• 2. George David Birkhoff, with H. S. Vandiver, On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Trans. Amer. Math. Soc. vol. 9 (1908) pp. 219-231.
• 3. George David Birkhoff, with H. S. Vandiver, Boundary value and expansion problems of ordinary linear differential equations, Trans. Amer. Math. Soc. vol. 9 (1908) pp. 373-395.
• 4. George David Birkhoff, with H. S. Vandiver, Existence and oscillation theorems for a certain boundary value problem, Trans. Amer. Math. Soc. vol. 10 (1909) pp. 259-270.
• 5. George David Birkhoff, with H. S. Vandiver, On the solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. vol. 12 (1911) pp. 103-127.
• 6. George David Birkhoff, with H. S. Vandiver, Note on the expansion problems of ordinary linear differential equations, Rend. Circ. Mat. Palermo vol. 36 (1913) pp. 115-126.
• 7. George David Birkhoff, with H. S. Vandiver, A theorem on series of orthogonal functions with an application to Sturm-Liouville series, Proc. Nat. Acad. Sci. U.S.A. vol. 3 (1917) pp. 656-659.
• 8. George David Birkhoff, with H. S. Vandiver, With R. E. Langer, The boundary problems and developments associated with a system of ordinary linear differential equations of first order, Proceedings of the American Academy of Arts and Sciences vol. 58 (1923) pp. 49-128.
• 9. George David Birkhoff, with H. S. Vandiver, With M. R. Hestenes, Natural isoperimetric conditions in the calculus of variations, Duke Math. J. vol. 1 (1935) pp. 198-286.
• 10. George David Birkhoff, with H. S. Vandiver, Singular points of ordinary linear differential equations, Trans. Amer. Math. Soc. vol. 10 (1909) pp. 436-470.
• 11. George David Birkhoff, with H. S. Vandiver, A simplified treatment of the regular singular point, Trans. Amer. Math. Soc. vol. 11 (1910) pp. 199-202.
• 12. George David Birkhoff, with H. S. Vandiver, A theorem on matrices of analytic functions, Math. Ann. vol. 74 (1913) pp. 122-133.
• 13. George David Birkhoff, with H. S. Vandiver, The generalized Riemann problem for linear differential equations and the allied problems for linear difference and q-difference equations, Proceedings of the American Academy of Arts and Sciences vol. 49 (1913) pp. 521-568.
• 14. George David Birkhoff, with H. S. Vandiver, Infinite products of analytic matricest Trans. Amer. Math. Soc. vol. 17 (1916) pp. 386-404.
• 15. George David Birkhoff, with H. S. Vandiver, General theory of linear difference equations, Trans. Amer. Math. Soc. vol. 12(1911) pp. 243-284.
• 16. George David Birkhoff, with H. S. Vandiver, Formal theory of irregular linear difference equations, Acta Math. vol. 54 (1930) pp. 205-246.
• 17. George David Birkhoff, with H. S. Vandiver, With W. J. Trjitzinsky, Analytic theory of singular difference equations, Acta Math. vol. 60 (1933) pp. 1-89.
• 18. George David Birkhoff, with H. S. Vandiver, Quelques théorèmes sur le mouvement des systèmes dynamiques, Bull. Soc. Math. France vol. 40 (1912) pp. 305-323.
• 19. George David Birkhoff, with H. S. Vandiver, Proof of Poincaré's geometric theorem, Trans. Amer. Math. Soc. vol. 14 (1913) pp. 14-22.
• 20. George David Birkhoff, with H. S. Vandiver, The restricted problem of three bodies, Rend. Circ. Mat. Palermo vol. 39 (1915) pp. 265-334. (Awarded the Quirini Stampalia Prize by the Royal Venice Institute of Science.)
• 21. George David Birkhoff, with H. S. Vandiver, Dynamical systems with two degrees of freedom, Trans. Amer. Math, Soc. vol. 18 (1917) pp. 199-300. (Awarded the first Bôcher Memorial Prize in 1923.)
• 22. George David Birkhoff, with H. S. Vandiver, Recent advances in dynamics, Science vol. 51 (1920) pp. 51-55.
• 23. George David Birkhoff, with H. S. Vandiver, Surface transformations and their dynamical applications, Acta Math. vol. 43 (1920) pp. 1-119.
• 24. George David Birkhoff, with H. S. Vandiver, An extension of Poincaré's last geometric theorem, Acta Math. vol. 47 (1925) pp. 297-311.
• 25. George David Birkhoff, with H. S. Vandiver, Stability and the equations of dynamics, Amer. J. Math. vol. 49 (1927) pp. 1-38.
• 26. George David Birkhoff, with H. S. Vandiver, Dynamical systems, Amer. Math. Soc. Colloquium Publications, vol. 9, New York, 1927.
• 27. George David Birkhoff, with P. A. Smith, Structure analysis of surface transformations, J. Math. Pures Appl. (9) vol. 7 (1928) pp. 345-379.
• 28. George David Birkhoff, with P. A. Smith, Une généralisation à n dimensions du dernier théorème de géométrie de Poincaré, C. R. Acad. Sci. Paris vol. 192 (1931) pp. 196-198.
• 29. George David Birkhoff, with P. A. Smith, Proof of a recurrence theorem for strongly transitive systems; Proof of the ergodic theorem, Proc. Nat. Acad. Sci. U.S.A. vol. 17 (1931) pp. 650-655; 656-660.
• 30. George David Birkhoff, with B. O. Koopman, Recent contributions to the ergodic theory, Proc. Nat. Acad. Sci. U.S.A. vol. 18 (1932), pp. 279-282.
• 31. George David Birkhoff, with D. C. Lewis, Jr., On the periodic motions near a given periodic motion of a dynamical system, Annali di Mat. Pura Appl. vol. 12 (1933) pp. 117-133.
• 32. George David Birkhoff, with D. C. Lewis, Jr., Sur le problème restreint des trois corps (Premier Mémoire), Annali della R. Scuola Normale Superiore Pisa (2) vol. 4 (1935) pp. 267-306.
• 33. George David Birkhoff, with D. C. Lewis, Jr., Nouvelles recherches sur les systèmes dynamiques, Mémoriae Pont. Acad. Sci. Novi Lyncaei vol. 1 (1935) pp. 85-216. (Crowned by the Pontifical Academy of Science.)
• 34. George David Birkhoff, with D. C. Lewis, Jr., Sur le problème restreint des trois corps (Second Mémoire), Annali della R. Scuola Normale Superiore Pisa (2) vol. 5 (1936) pp. 1-42.
• 35.George David Birkhoff, wWith D. C. Lewis, Jr., Some unsolved problems of theoretical dynamics, Science vol. 94 (1941) pp. 598-600.
• 36. George David Birkhoff, with D. C. Lewis, Jr., Books on relativity, Bull. Amer. Math. Soc. vol. 28 (1922) pp. 215-221.
• 37. George David Birkhoff, with D. C. Lewis, Jr., The origin, nature and influence of relativity (Lowell Institute Lectures), New York, 1925.
• 38. George David Birkhoff, with D. C. Lewis, Jr., A theory of matter and electricity, Proc. Nat. Acad. Sci. U.S.A. vol. 13 (1927) pp.160-165.
• 39. George David Birkhoff, with D. C. Lewis, Jr., The hydrogen atom and the Balmer formula, Proc. Nat. Acad. Sci. U.S.A. vol. 13 (1927) pp. 165-169.
• 40. George David Birkhoff, with D. C. Lewis, Jr., A mathematical critique of some physical theories, Bull. Amer. Math. Soc. vol. 33 (1927) pp. 165-181. (Awarded the annual prize of the American Association for the Advancement of Science.)
• 41. George David Birkhoff, with D. C. Lewis, Jr., Some remarks concerning Schrödinger's wave equation, Proc. Nat. Acad. Sci. U.S.A. vol. 19 (1933) pp. 339-344.
• 42. George David Birkhoff, with D. C. Lewis, Jr., Electricity as a fluid, Journal of the Franklin Institute vol. 226 (1938) pp. 315-325.
• 43. George David Birkhoff, with D. C. Lewis, Jr., Matter, electricity and gravitation in flat space-time, Proc. Nat. Acad. Sci. U.S.A. vol. 29 (1943) pp. 231-239.
• 44. George David Birkhoff, with D. C. Lewis, Jr., The mathematical nature of physical theories, American Scientist vol, 31 (1943) pp. 281-310. 44a With D. C. Lewis, Jr., El concepto matemático de tiempo y la gravitación, Boletin de la Sociedad Matemática Mexicana vol. 1 (1944) pp. 1-24.
• 45. George David Birkhoff, with O. D. Kellogg, Invariant points in function space, Trans. Amer. Math. Soc. vol. 23 (1922) pp. 96-115.
• 46. George David Birkhoff, with O. D. Kellogg, A determinant formula for the number of ways of coloring a map, Ann. of Math. vol. 14 (1912) pp. 42-46.
• 47. George David Birkhoff, with O. D. Kellogg, The reducibility of maps, Amer. J. Math. vol. 35 (1913) pp. 115-128.
• 48. George David Birkhoff, with O. D. Kellogg, On the number of ways of coloring a map, Proc. Edinburgh Math. Soc. (2) vol. 2 (1930) pp. 83-91.
• 49. George David Birkhoff, with O. D. Kellogg, On the polynomial expressions for the number of ways of coloring a map, Annali della R. Scuola Normale Superiore Pisa (2) vol. 3 (1934) pp. 1-19.
• 50. George David Birkhoff, with O. D. Kellogg, General mean value and remainder theorems with applications to mechanical differentiation and quadrature, Trans. Amer. Math. Soc. vol. 7 (1906) pp. 107-136.
• 51. George David Birkhoff, with O. D. Kellogg, Aesthetic measure, Cambridge, 1933.
• 52. George David Birkhoff, with O. D. Kellogg, A set of postulates for plane geometry based on scale and protractor, Ann. of Math. vol. 33 (1932) pp. 329-345.
• 53. George David Birkhoff, with Ralph Beatley, Basic geometry, New York, 1940.
• 54. George David Birkhoff, with Ralph Beatley, Fifty years of American mathematics, Amer. Math. Soc. Semicentennial Publications, vol. 2, 1938, pp. 270-315.