Professor Jack K. Hale

And

His Mathematics

by

Shui-Nee Chow at

ICMC Summer Meeting on Differential Equations

Sao Carlos, Brazil, 2008

On The Occasion

Of His

Eightieth Birthday

His Education

• Birth Date: Oct 3, 1928

• Birth Place: Carbonglow, KY, USA

• Small coal mining community• Father, manager of a general store• Childhood • One location to another

His Education

•1939 － 1945，World war II•1944 - Martin High School, Martin, KY

•44 - 49 Berea College

Berea College

• founded in 1855, abolitionists

• liberal arts college in Berea, Kentucky (south of Lexington)

• interracial and coeducational

• funding students from low-income families

Berea College

• work college

• min 10 hr/week : room & board

• 140 labor activities

• low income: < $34K, family of 4

Berea College

• 1904 Kentucky, Day Law

• Berea, pure white

• 1950 Day Law amended

• 1/2 B dollars endowment

• 14th largest in US, private colleges & U

Notable Alumni• John B. Fenn - winner of the 2002 Nobel Prize in

chemistry

• Juanita M. Kreps - U.S. Secretary of Commerce under President Jimmy Carter

• Naomi Tutu - daughter of Archbishop Desmond Tutu and activist

• Finley Hamilton - United States Representative from Kentucky

• Keven McQueen, author of several books chronicling violent crime in pre-20th century Kentucky

His Education

• 44 - 48 Hazel Reynolds

• 49 Graduation and Wedding

• 50 - 53 Korean War

• 49 - 53 Purdue University

• 53 - 54 Instructor, Purdue

• 54 - 57 Sandia

• 57 - 58 Remington Rand Univac

• 58 - 64 RIAS

His Work Experience I

S. Jones

• 64 - 88 Brown University

• 88 - 98 Georgia Tech

• 68 - 69 UCLA

• 71 - 72 Dini Institute

• 61, 71, 75 Brazil

• 97 Kloestermann Professorship, Leiden

His Work Experience II

His Teachers and Colleagues

• L. Cesari (nonlinear oscillations)

• S. Lefschez (qualitative theory)

• J. LaSalle (attractors)

His Awards

• 65, Chauvenet Prize (with LaSalle)(1965)

• 79, Guggenheim Fellowship

• 86, British Carneige Fellowship

• 91, Sigma Xi sustained research award

His Memberships

• 79, Corresponding Member of the Brazilian Academy of Science

• 87, Honorary Fellow of Royal Society of Edinburgh

• 92, Foreign Member Polish Academy of Science

His Honorary Doctor Degrees

• 82, Ghent, Belgium

• 88, Stuttgart, Germany

• 91, Univ. Tecnia de Lisboa, Portugal

• 99, Rostock, Germany

• 00, Clark University, Worcester MA

His Research - I

• Integral manifolds of perturbed differential systems. Ann. of Math, 1961

• A class of functional equations of neutral type. Memoirs of AMS, 1967 (K. Meyer)

His Research - II

• Alternative problems for nonlinear functional equations. J. Differential Equations 1968 (S. Bancroft, D. Sweet)

• Theory of a general class of dissipative processes. J. Math. Anal. App., 1972 J. LaSalle, M. Slemrod)

His Research - III

• Coincidence degree and periodic solutions of neutral equations. J. Differential Equations, 1974 (J. Mawhin)

• Applications of generic bifurcations. I. Arch. Rational Mech. Anal., 1975 (S. Chow, J. Mallet-Paret)

His Research - IV

• An example of bifurcation to homoclinic orbits. J. Differential Equations, 1980 (S. Chow, J. Mallet-Paret)

• Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation. J. Differential Equations, 1988 (G. Raugel)

His Research - V

• Slow-motion manifolds, dormant instability, and singular perturbations. J. Dynam. Differential Equations, 1989 (G. Fusco)

• A damped hyperbolic equation with critical exponent. Comm. Partial Differential Equations, 1992 (J. Arrieta, A. Carvalho)

His Books I

• Oscillation in Nonlinear Systems, 1963

• Ordinary Differential Equations, 1969

• Functional Differential Equations, 1977

• Methods of Bifurcation Theory, 1981 (S. Chow)

• Introduction to Infinite Dimensional Systems, 1984 (L. Magalhaes, W. Oliva)

His Books II

• Dissipative Dynamical Systems, 1988

• Dynamics and Bifurcations, 1991 (H. Kocak)

• Introduction to Functional Differential Equations, 1993 (S. Lunel)

• Infinite Dimensional Differential Equations, 2002 (L. Magalhaes, W. Oliva)

His Citations

• MathSciNet

• Jan 9. 2008

• Publications: 267

• Citations : 3,232

• By 2,136 authors

His Ph. D. Students

•1 - RIAS

•36 - Brown

•10 - Georgia Tech

1963 Carlos Imaz (Univ. Autonoma, Mexico)1965 Carlos Perello (Univ. Autonoma, Barcelona)1966 Nathanial Chafee (Georgia Tech)1967 Robert Grafton (NSF Washington)1967 James Hurt (Computing, Ohio)1968 Stephen Bancroft (Iowa)1969 Daniel Henry - deceased (Univ. Sao Paulo, Brazil)1969 Daniel Sweet - deceased (Univ. Maryland)1969 Marianito Cruz -deceased (Phillipines)

1970 William Melvin (Los Alamos)1971 Alan Hausrath (Idaho State Univ.)1973 Orlando Lopes (Univ. Campinas, Brazil)1974 Julio Ruiz-Claeyssen (Porto Allegro, Brazil)1976 Pedro Martinez-Amores (Granada, Spain)1976 Richard Silkowski (General Electric, New York)1976 Stephen List1977 Paulo Lima (Univ. Recife, Brazil)1978 Nicholas Alikakos (Tech. Univ. Athens, North Texas State)1978 Gene Cooperman (GTE, Boston)

1979 Cerino Avellar (Federal Univ. S~ao Carlos, Brazil)1979 Gaspar Ruas Filho (Univ. S~ao Paulo, S~ao Carlos)1979 Kris Rybakowski (Univ. Rostock, Germany)1980 Paul Massatt (Aerospace, Pasadena)1980 Lawrence Turyn (Wright State, Dayton)1981 Jose Vegas (Compultense, Madrid)1982 Luis Magalh~aes (Inst. Tecnico, Lisbon)1983 Arnaldo Nascimento (Federal Univ. S~ao Carlos)1984 Jurgen Quandt (Germany)1985 Miguel Blasquez -deceased (Univ. Veracruz, Chile)

1985 Georgia Fusco (Univ. L'Aquila, Italy)1985 Xiao-Biao Lin (North Carolina State)1985 Carlos Rocha (Inst. Tecnico, Lisbon)1985 Natalia Sternberg (Clark Univ. Worchester)1986 Margaret Memory (Alabama)1988 Kunimochi Sakamoto (Hiroshima Univ., Japan)1989 Yulin Cao (Long Island NY)

1991 Jose Arrieta (Compultense, Madrid)1992 Alexandre Carvalho (Univ. S~ao Paulo, S~ao Carlos)1992 M. Chen (1/2 with X.-Y. Chen) (NCS, Winston-Salem)1992 Brad Lehman (1/2 with E. Verreist, EE) (Northeastern)1993 Gwendolyn Hines (Univ. Nebraska, Lincoln)1993 Sergio Oliva (Univ. S~ao Paulo SP)1994 Juan Pinto (Inst. Tecnico, Lisbon)1998 Bin Tan1998 Domingo Salazar (England and Spain)2000 Marion Weedermann (Dominican Univ., Illinois)

• Mallet-Paret

• Mischaikow

• Perieira

• Yi

• Lu

• Lunel

• Huang

• Li

• Neves

Some of his Postdocs

Thank you, Jack!