My research is focused in two areas. The chronologically older of the two is
chaos theory. Here I am currently interested in understanding the degree of
generality of statistical robustness for chaotic systems. The other area is the
computational complexity of real number algorithms. Here with co-workers I
am trying to build the foundations of a complexity theory appropriate to
problems of science and engineering. Particular interests are the P versus NP
problem of theoretical computer science in this new context and Newton type
methods for solving systems of equations.
My wife, Beate Echols and I collect art from around the world. You can see our collection
at Beate's web site and
Our Cuban art web site.
PDF files of selected preprints.
PDF file of Invariant manifolds, (with M. Hirsch and C. Pugh), Springer-Lecture Notes on Mathematics, #583, Heidelberg 1977.
email: shub.michael@gmail.com
phone:416 946 0323
fax: 416 978 4107
address:
Mathematics Department
University of Toronto
40 St George Street
Toronto, ON, M5S 2E4, Canada