Topics in Linear Dynamical Systems
AbstractA linear dynamical system is a discrete- or continuous-time system whose dynamics is given by a linear function of the current state. Examples include Markov chains, linear recurrence sequences (such as the Fibonacci sequence), and linear differential equations.
This project involves investigating the decidability and complexity of various reachability problems for linear dynamical systems. It would suit a mathematically oriented student. Linear algebra is essential, and number theory or complexity theory is desirable.
A relevant paper is Ventsislav Chonev, Joël Ouaknine, James Worrell: The orbit problem in higher dimensions. STOC 2013: 941-950.