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math.DS2026
Functional correlation bound for random Lasota--Yorke maps with holes and its applications to conditional normal approximations
Juho Leppänen, Yuto Nakajima, Yushi Nakano
This paper investigates the statistical properties of random open dynamical systems generated by families of Lasota--Yorke maps. Open systems, in which trajectories may escape thro…
math.DS2025
On the topology of the limit sets of non-autonomous iterated function systems
Yuto Nakajima, Takayuki Watanabe
Since Mandelbrot's seminal work, there has been growing interest in the geometric nature of fractals. While the topological properties of the limit sets of IFSs have been studied -…
math.DS2025
Error bounds in a smooth metric for Brownian approximation of dynamical systems via Stein's method
Juho Leppänen, Yuto Nakajima, Yushi Nakano
We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit th…