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.[8] 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.[9] 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.[10]
Devaney hairs, a fractal structure in certain Julia sets, are named after Devaney, who was the first to investigate them.[3][11]
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][3] He was president of the Mathematical Association of America from 2013 to 2015.[4][5]
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.[3]
Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics (Addison-Wesley, 1990)[19]
A First Course in Chaotic Dynamical Systems: Theory and Experiment (Addison-Wesley, 1992)[20]
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)[21]
Research papers
Some of the more highly cited of Devaney's research publications include:
^Banks, John; Dragan, Valentina; Jones, Arthur (2003), Chaos: A Mathematical Introduction, Australian Mathematical Society Lecture Series, vol. 18, Cambridge University Press, p. viii, Bibcode:2003cmi..book.....B, ISBN9780521531047, 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.
