April 24, 2025
Megan Triplett '25 will present Finite and Countable Dynamical Systems. Pizza provided. Everyone welcome to attend.
A dynamical system is a function f from a set X to itself. From a given starting element x in X, this function is then iterated — that is, we apply the function repeatedly to produce orbits x, f(x), f(f(x))=f2(x). It is possible for orbits to be periodic. In our investigations, X is either a finite set or a countably infinite set, and, in the countably infinite case, we focus on dynamical systems that exhibit behavior similar to finite dynamical systems. In particular, we illustrate that every orbit in a finite dynamical system is eventually periodic, and we outline conditions under which countably infinite dynamical systems exhibit the same property. To relate such dynamical systems to finite ones, we introduce bounds on the eventual behavior of countably infinite systems that depend on the function on which it is constructed. From there, we investigate a particular finite dynamical system on the natural numbers: sums of functions of digits, and we focus on finding a bound for such systems. We introduce a bound that is easier to compute than Stewart's tight bound C and tighter than Kiss's loose bound. Then, to discuss countable sets that need not be a subset of the natural numbers, we introduce discrete Lyapun
Further information
- Location: Tome 115
- Time: 12:00 pm - 1:00 pm
- Cost: Free