May 2, 2019
Mengting Chao '20 will present "Dynamics of the Taylor Series Approximation of the Dixon Elliptic Functions". Free pizza and everyone welcome to attend.
The function T_c (x)=c-x^3/3+x^6/18 is a Taylor series approximation of a Dixon elliptic function at the origin, where each c value corresponds to a different Dixon elliptic function. One thing that makes Tc complicated to study is that we cannot solve algebraically for its fixed and periodic points, which is typically the first step to explore a dynamical system resulting from function iteration. Instead, we use a theorem about negative Schwarzian derivatives to find an upper bound on the number of attracting cycles of Tc. Then we utilize the orbits of critical points to explore the location of attracting fixed and periodic points which form those attracting cycles. We also show the existence of a saddle-node bifurcation and a period-doubling bifurcation for Tc.
Further information
- Location: Tome 117
- Time: 12:00 pm - 1:00 pm
- Cost: Free