Project description
A mathematical crystal ball for the future and the past
Most real-life processes are dynamical systems, systems that evolve over time and in a defined 'state space' (akin to the various states the system can be in) according to a fixed rule. They are related sets of processes through which matter or energy flows, continually changing. Populations, epidemics and economies at all scales are examples of dynamical systems. Discrete dynamical systems evolve in discrete time steps. The EU-funded LISEDIDYS project is investigating the limit sets of such systems into the future or the past as well as where they end up after an infinite amount of time has passed. Applying a variety of mathematical techniques and methods, the project's outcomes will enhance understanding of the long-term behaviour of discrete dynamical systems.
Objective
The proposed project aims to deepen our knowledge on limit sets which will provide a better understanding of the long term behavior of a discrete dynamical system. We will investigate the topological size and structure of basins of limit sets and study the properties of statistical limit sets and limit sets of backward trajectories. We will search for a criterion allowing to decide whether a given closed invariant set is a limit set of some backward trajectory. The focus will be on the low-dimensional dynamical systems such as interval maps, maps acting on the circle, graphs, dendrites, Cantor space. We will use methods and techniques from topological dynamics and ergodic theory, including combinatorial and symbolic dynamics, shadowing, specification property, invariant measures and generic points.
Fields of science
Programme(s)
Funding Scheme
MSCA-IF-EF-CAR - CAR – Career Restart panelCoordinator
30-059 Krakow
Poland