My main objects of study are dynamical systems. A dynamical system has a state, represented by vector of objects (typically integers or real numbers) and the evolution rule of the system is a function that describes the future states from the current state. I mainly study continuous system, either in space (the state space is a vector of real numbers) or in time (the evolution rule is given by a differential equation). Since dynamical systems are (too) general, my focus is on the polynomial and linear systems. Furthermore, my research focuses on three related aspects of dyanical systems: