no code implementations • 19 Feb 2021 • Julien Cassaigne, Sébastien Labbé, Julien Leroy
The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set $\{1, 2\}^\mathbb{N}$ of directive sequences.
Dynamical Systems Combinatorics 37B10 (Primary) 68R15, 11J70, 37H15 (Secondary)
no code implementations • 7 Dec 2020 • Sébastien Labbé
The goal of this chapter is to illustrate a generalization of the Fibonacci word to the case of 2-dimensional configurations on $\mathbb{Z}^2$.
Dynamical Systems 37B50 (Primary) 52C23, 28D05 (Secondary)
1 code implementation • 3 Jun 2019 • Sébastien Labbé
As a consequence, $\mathcal{P}_0$ is a Markov partition for the associated toral $\mathbb{Z}^2$-rotation $R_0$.
Dynamical Systems Metric Geometry 37A05 (Primary) 37B51, 52C23 (Secondary)
1 code implementation • 14 Mar 2019 • Sébastien Labbé
We define another partition $\mathcal{P}_\mathcal{U}$ and a $\mathbb{Z}^2$-rotation on $\mathbb{T}^2$ whose associated symbolic dynamical system is equal to a minimal and aperiodic Wang shift defined by 19 Wang tiles.
Dynamical Systems Metric Geometry
