arXiv subjects
Publications and source records attributed to Yann Jullian.
We consider a mathematical model of the breakout game where $\mathbb{R}^2$ is covered by unit square bricks everywhere except in one place. We introduce elementary blocks (particular sets of bricks) in order to describe a family of periodic (in a breakout-appropriate sense) orbits. Necessary and sufficient conditions for slopes (the initial direction of the ball) to produce these orbits are given.
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.
We give an algorithm for finding the index of a positive outer automorphism of the free group, and prove the algorithm exits in a finite time.
This article introduces tree substitutions as a tool to give explicit geometric representations of the dynamical systems generated by a particular set of automorphisms of the free group.