Robert L. Devaney

Robert Luke Devaney (born 1948) is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University. His research involves dynamical systems and fractals.[1]

Robert L. Devaney
Devaney in 1973
Born (1948-04-09) April 9, 1948
Methuen, Massachusetts, US
Alma materUniversity of California, Berkeley
Scientific career
FieldsMathematics
InstitutionsBoston University
Doctoral advisorStephen Smale

Education and career

Devaney was born on April 9, 1948, and grew up in Methuen, Massachusetts.[2]

Devaney graduated in 1969 from the College of the Holy Cross,[3][4] and earned his Ph.D. in 1973 from the University of California, Berkeley under the supervision of Stephen Smale.[5] Before joining the faculty at Boston University, he taught at Tufts University, Northwestern University, and the University of Maryland, College Park.[3][4]

Mathematical activities

Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory.[6] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set will eventually hit the other set), and its periodic orbits form a dense set.[7] Later, it was observed that this definition is redundant: sensitive dependence on initial conditions follows automatically as a mathematical consequence of the other two properties.[8]

Devaney hairs, a fractal structure in certain Julia sets, are named after Devaney, who was the first to investigate them.[2][9]

As well as research and teaching in mathematics, Devaney's mathematical activities have included organizing one-day immersion programs in mathematics for thousands of Boston-area high school students, and consulting on the mathematics behind media productions including the 2008 film 21 and the 1993 play Arcadia.[1][2] He was president of the Mathematical Association of America from 2013 to 2015.[3][4]

Awards and honors

In 1995, Devaney won the Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching of the Mathematical Association of America.[10] In 2002 Devaney won the National Science Foundation Director's Award for Distinguished Teaching Scholars.[1][11] He was named the inaugural Feld Professor in 2010.[1]

In 2008, a conference in honor of Devaney's 60th birthday was held in Tossa de Mar, Spain. The papers from the conference were published in a special issue of the Journal of Difference Equations and Applications in 2010, also honoring Devaney.[2]

In 2012 he became one of the inaugural fellows of the American Mathematical Society.[12]

Selected publications
Books

Devaney is the author of books on fractals and dynamical systems including:

  • An Introduction to Chaotic Dynamical Systems (Benjamin/Cummings 1986; 2nd ed., Addison-Wesley, 1989; reprinted by Westview Press, 2003)[13][14][15]
  • The Science of Fractal Images (with Barnsley, Mandelbrot, Peitgen, Saupe, and Voss, Springer-Verlag, 1988)[16]
  • Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics (Addison-Wesley, 1990)[17]
  • A First Course in Chaotic Dynamical Systems: Theory and Experiment (Addison-Wesley, 1992)[18]
  • Fractals: A Tool Kit of Dynamics Activities (with J. Choate and A. Foster, Key Curriculum Press, 1999)
  • Iteration: A Tool Kit of Dynamics Activities (with J. Choate and A. Foster, Key Curriculum Press, 1999)
  • Chaos: A Tool Kit of Dynamics Activities (with J. Choate, Key Curriculum Press, 2000)
  • The Mandelbrot and Julia Sets: A Tool Kit of Dynamics Activities (Key Curriculum Press, 2000)
  • Differential Equations (with P. Blanchard and G. R. Hall, 3rd ed., Brooks/Cole, 2005)
  • Differential Equations, Dynamical Systems, and an Introduction to Chaos (with Morris Hirsch and Stephen Smale, 2nd ed., Academic Press, 2004; 3rd ed., Academic Press, 2013)[19]
Research papers

Some of the more highly cited of Devaney's research publications include:

  • Devaney, Robert L. (1976), "Homoclinic orbits in Hamiltonian systems", Journal of Differential Equations, 21 (2): 431–438, Bibcode:1976JDE....21..431D, doi:10.1016/0022-0396(76)90130-3, MR 0442990.
  • Devaney, Robert L. (1976), "Reversible diffeomorphisms and flows", Transactions of the American Mathematical Society, 218: 89–113, doi:10.2307/1997429, MR 0402815.
  • Devaney, Robert L. (1980), "Triple collision in the planar isosceles three-body problem", Inventiones Mathematicae, 60 (3): 249–267, Bibcode:1980InMat..60..249D, doi:10.1007/BF01390017, MR 0586428.
  • Devaney, Robert L.; Krych, Michał (1984), "Dynamics of exp(z)", Ergodic Theory and Dynamical Systems, 4 (1): 35–52, doi:10.1017/S014338570000225X, MR 0758892.
gollark: Is the dungeon secretly made of cardboard?
gollark: I conjure additional footwear, d6.
gollark: Maybe it was a decoy spike.
gollark: Hmm.
gollark: I conjure additional spike-proof footwear, d6.

References
  1. Barlow, Rich (February 18, 2000), "CAS Names First Feld Family Professor: Robert Devaney makes fractals crackle, starting in high school", BU Today, Boston University.
  2. Keen, Linda (2010), "Introduction to the Robert Devaney special issue", Journal of Difference Equations and Applications, 16 (5–6): 407–409, doi:10.1080/10236190903260838.
  3. Brief vita: Robert L. Devaney, retrieved 2015-09-28.
  4. Robert L. Devaney, About MAA: Governance, Mathematical Association of America, retrieved 2015-09-28.
  5. Robert L. Devaney at the Mathematics Genealogy Project
  6. Banks, John; Dragan, Valentina; Jones, Arthur (2003), Chaos: A Mathematical Introduction, Australian Mathematical Society Lecture Series, 18, Cambridge University Press, p. viii, ISBN 9780521531047, Although there are several competing definitions of chaos, we concentrate here on the one given by Robert Devaney, which avoids the use of measure theory and uses only elementary notions from analysis.
  7. Boccara, Nino (2010), Modeling Complex Systems, Graduate Texts in Physics (2nd ed.), Springer-Verlag, p. 180, ISBN 9781441965622.
  8. Banks, J.; Brooks, J.; Cairns, G.; Davis, G.; Stacey, P. (1992), "On Devaney's definition of chaos", The American Mathematical Monthly, 99 (4): 332–334, doi:10.2307/2324899, MR 1157223.
  9. Rempe, Lasse; Rippon, Philip J.; Stallard, Gwyneth M. (2010), "Are Devaney hairs fast escaping?", Journal of Difference Equations and Applications, 16 (5–6): 739–762, arXiv:0904.1403, doi:10.1080/10236190903282824, MR 2675603.
  10. Deborah and Franklin Tepper Haimo Award – List of Recipients, Mathematical Association of America, retrieved 2015-09-28.
  11. BU professor wins NSF teaching award, Boston University, February 2007, retrieved 2015-09-28.
  12. List of Fellows of the American Mathematical Society, American Mathematical Society, retrieved 2015-09-28
  13. Review of An introduction to chaotic dynamical systems by Richard C. Churchill (1987), MR0811850.
  14. Review of An Introduction to Chaotic Dynamical Systems by Philip Holmes (1987), SIAM Review 29 (4): 654–658, JSTOR 2031218.
  15. Eckmann, Jean‐Pierre (1987). "Review of An Introduction to Chaotic Dynamical Systems by Robert L. Devaney". Physics Today. 40 (7): 72. doi:10.1063/1.2820117. ISSN 0031-9228.
  16. Review of The Science of Fractal Images by P. D. F. Ion (1992), MR0952853.
  17. Review of Chaos, Fractals, and Dynamics by Thomas Scavo (1991), The College Mathematics Journal 22 (1): 82–84, doi:10.2307/2686745.
  18. Review of A First Course in Chaotic Dynamical Systems by Frederick R. Marotto (1994), MR1202237.
  19. Review of Differential Equations, Dynamical Systems, and an Introduction to Chaos by Michael Hurley (2005), MR2144536.
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