Graduate Student
Paper Session
Non-local Cellular Automata over groups
In this paper, we study Cellular Automata with unbounded neighborhoods whose cells each contain an element of a group, and are almost everywhere the identity. This last property allows effective computation. We prove some dynamical and topological properties, including the existence of certain dense sets of orbits. Finally, we describe properties of a class of 1-dimensional cellular automata involving the ring of integers.
Evolution of the McMullen Domain for Singularly Perturbed Rational Maps.
Abstract: We present examples of families of rational functions for which small perturbations produce important changes on their dynamics. We also discuss the stability of these changes focusing mainly on the topological characteristics of the interesting Julia sets that may arise.
8:40 – 8:55 am - Benjamin
Hutz,
Arithmetic dynamics on a class of K3 surfaces
An important topic in arithmetic dynamics is the study of the arithmetic properties of periodic points. Much work has been done in the case of rational maps on the projective line. After briefly discussing this case, I will describe dynamical systems on a certain class of K3 surfaces and discuss properties of their periodic points.