MAT335H1 Lecture Notes - Lecture 5: Parametric Family, Quadratic Function
Document Summary
We are already introduced to the concept of bifurcation in notes 1 and 2. A parametric family of solutions change behavior as a result of change in the parameter. Xed point (resp. repelling) comes an attracting 2-cycle (resp. repelling), and at the same time the. Xed point ceases to be attracting (resp. repelling. ) For the quadratic function qc this is taking place at c = 3: be sure to know how to come to this conclusion. Indeed, try to show that for all x0 outside this interval, qn c (x0) will diverge (to + ). This is of course just because the graph of qc(x) is symmetric about the y axis. So in terms of dynamical activities this interval is a tight interval. 4 the 2-cycle is unique. (why?: note that for the values 5, there is an interesting observation made in remark 3, page 62, that period doubling takes place when. (x0) = 0 then this process may.
