Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the " geometry " of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed not only for one-dimensional mappings, unimodal as well as those with multiple critical points and discontinuities, but also for some two-dimensional mapping...

Robert L. Devaney, Boston University Synopsis As so often happens in mathematics, there is a surprising connection between two quite distinct subfields of dynamical systems theory, namely the structure of the automorphism group of the one sided shift map on d-symbols and the topology of the analogue of the Mandelbrot set for degree d polynomials of one complex variable. In this lecture we will ...

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchroni...