3 papers
math.DS2026
Topology of slices through the Sierpiński tetrahedron
Yuto Nakajima, Takayuki Watanabe
We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each , we study the Čech (co)homology group of the slice at height . We show tha…
math.DS2024
Bowen's formula for a rational graph-directed Markov system
Tadashi Arimitsu, Johannes Jaerisch, Hiroki Sumi +1
We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating co…
math.DS2018
Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity
Hiroki Sumi, Takayuki Watanabe
We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps are related to Markov chains. Our motivation is to generalize the facts which hold in i…