3 papers
math.DS2025
Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set
Hugo Marsan, Mathieu Sablik
Consider the dynamical system constitued by a continuous function where is a finite alphabet. The perturbed counte…
nlin.CG2025
A perturbed cellular automaton with two phase transitions for the ergodicity
Hugo Marsan, Mathieu Sablik, Ilkka Törmä
The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been…
math.DS2024
Characterization of the set of zero-noise limits measures of perturbed cellular automata
Hugo Marsan, Mathieu Sablik
We add small random perturbations to a cellular automaton and consider the one-parameter family parameterized by where is the level of noise. The object…