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Longest increasing subsequences of dyadic-type chaotic orbits
Shinsuke Iwao, Fumihiko Nakamura, Yushi Nakano
This paper studies the longest increasing subsequence (LIS) problem for sequences generated by dyadic-type chaotic interval maps. Starting from a single point chosen un…
A robust obstruction to full strong pluripotency for wild blender-horseshoes
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
Suppose that is a closed manifold of dimension greater than two and . We show that there exists a -diffeomorphism with a wild affine blende…
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…
Non-existence of Lyapunov exponents in the Newhouse domain
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
We show that within the Newhouse domain of surface diffeomorphisms (), there exists a dense subset such that for any , Lyapu…
Finitude of physical measures for Markovian random maps
Pablo G. Barrientos, Dominique Malicet, Fumihiko Nakamura +2
We study the finiteness of physical measures for skew-product transformations associated with discrete-time random dynamical systems driven by ergodic Markov chains. We develop…
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…