3 citations · 7 across the 5 of their papers we have counts for
5 papers
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…
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…
On the stochastic bifurcations regarding random iterations of polynomials of the form
Takayuki Watanabe
In this paper, we consider random iterations of polynomial maps where are complex-valued independent random variables following the uniform distribution on the clo…
Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
Hiroki Sumi, Takayuki Watanabe
We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with…
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…