Research

Projects

• Bounded noise dynamical systems

We are studying a simple problem: what are the properties of the support of a process when a dynamical system involves a bounded perturbation? 

It is foreseeable that this problem is not only a natural mathematical question but also a common phenomenon in physics, science, and engineering. Currently, we are focusing on several directions: 

(i) By studying how the boundary of a set evolves through the boundary map, we aim to understand the properties of set-valued dynamical systems. 

(ii) How does topological bifurcation occur under changes in different parameters? 

(iii) We are attempting to prove that the system is asymptotically periodic.

• A bridge from fractal geometry to graph theory: General Iterated Graph Systems

General Iterated Graph Systems is a model where, given prefixed rule graphs, graph fractals can be constructed through iterative vertex substitution or edge substitution. 

At first glance, you might find this model quite natural and simple, but if you are willing to take a minute to think deeply, a hundred questions arise that need to be answered: combinatorial properties, fractal dimensions, random walks, statistical physics... 

Perhaps we should be more astonished by the fact that human beings do not yet know all the answers to these questions.