Smooth equivalence of expanding maps of the circle

Dynamical Systems Working Seminar
Friday, April 7, 2017 - 3:05pm
1 hour (actually 50 minutes)
Skiles 254
School of Math, Georgia Tech
It is well known  that periodic orbits give all the information about dynamical systems, at least for expanding maps, for which the periodic orbits are dense. This turns out to be true in dimensions 1 and 2, and false in dimension 4 or higher.We will present a proof  that  two $C^\infty$ expanding maps of the circle, which are topologically equivalent are $C^\infty$ conjugate if and only if the derivatives or the return map at periodic orbits are the same.