Thomas Ohlson Timoudas: Cantor sets, shift maps and chaos
Time: Fri 2016-10-21 13.15 - 14.15
Location: Room 3418, Lindstedtsvägen 25, 4th floor, Department of Mathematics, KTH
Participating: Thomas Ohlson Timoudas, KTH
In dynamics we study the long-term behaviour of orbits, namely the distribution of the sets Orb(x) = {x, f(x), f(f(x)), ...} of iterates for some specified (continuous) map f: X -> X.
Invariant sets (closed sets U satisfying f(U) = U) provide us a notion of subspace. I will show how Cantor sets sometimes naturally appear as invariant sets, even for very simple maps f.
The quadratic map f(x) = ax(1-x) will take center stage in this surprising drama, featuring the shift map in the supporting role.