People
Zbigniew (Ziggy) Nitecki
Professor, Transfer of Credit & Distribution Advisor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Room 214
Medford, MA 02155
Email @tufts.edu:
zbigniew.nitecki
Phone: 6176273843
Personal site
Expertise:
Dynamical systems, especially in dimensions 1 and 2; braids;
combinatorial/geometric group theory; graphs
Research:
In mathematics, the term dynamical systems refers to models which
change in time according to their configuration momenttomoment:
for example, the velocities of planets in a solar system are ruled
by gravitational forces, which in turn are determined by the
relative positions of the planets; as another example, the net
growth rates of different populations in an ecosystem are ruled by
competition for space, food and other resources, which in turn is
determined by the sizes of these populations at any moment. This
information loopthe components of the system change according to
rules determined by the components themselvespresents a
mathematical conundrum, formulated either as a system of
differential equations or the iteration of some function or
algorithm. Certain classes
of dynamical systems (in particular "linear" systems) can be
understood explicitly using general methods, but numerous nonlinear
examples present exceptional cases that can only be understood, if
at all, by ad hoc means.
Starting in the 1960's two groupsone in Berkeley (where I was a
graduate student), the other in Moscowdeveloped a general theory
of nonlinear dynamical systems, focusing especially on identifying
two kinds of systems: those which are structurally stabletheir
qualitative features (for example, that the system eventually
settles into static equilibrium or regular oscillation) are robust
under small changes in the structure of the systemand those which
are genericthey exhibit typical behavior, in the sense that every
system can, via a small change in structure, be transformed into a
generic one. This program has contributed a number of deep insights
about dynamical systems, the most influential of which is the
distinction between determinism and predictability: systems built on
an entirely deterministic setup can nevertheless behave in a manner
so complex that only aggregate, statistical predictions of the
behavior are possible: this comes under the rubric of chaos.
My own work has followed several threads, for the most part pushing
parts of this program in new directions:
 Onedimensional systems
 Noncompact systems
 Noninvertible systems
 Topological entropy
 Geometric group theory
I have also written a number of expository books. Differentiable
Dynamics (MIT Press, 1972), the first booklength exposition of the
program sketched above, was translated into Russian and Chinese in
the mid1970's. A First Course in Differential Equations (Saunders,
1984, 1988, 1992), coauthored with Marty Guterman, was used by many
departments (including ours) as the text for the last math course
most engineers take. Calculus Deconstructed (MAA, 2009) is a
rigorous singlevariable calculus text which I developed for the
first semester of our Honors Calculus sequence (Math 39); the
multivariable followup, Calculus in 3D, is in the late stages of
development.
Since 2008, I have been a member of the board of the Somerville
Mathematics Fund, a volunteer organization affiliated with Dollars
for Scholars; we award small grants to mathematics teachers in
Somerville schools and scholarships to college students from
Somerville who are working at STEM majors. Since 2012 I am the
Associate Treasurer of the American Mathematical Society.
