# Yushi NAKANO

Last updated: Dec 30, 2019 at 15:17

Name Yushi NAKANO yushi.nakanotsc.u-tokai.ac.jp Tokai University Department of Mathematics Lecturer Doctor(Kyoto University)

## Research Areas

• Mathematics / Basic analysis / Dynamical systems theory, ergodic theory

## Published Papers

Yushi Nakano, Kenichiro Yamamoto
Dec 2019
For any transitive piecewise monotonic map for which the set of periodic
measures is dense in the set of ergodic invariant measures (such as linear mod
transformations and generalized -transformations), we show that the
set of points fo...
Pablo G. Barrientos, Shin Kiriki, Yushi Nakano, Artem Raibekas, Teruhiko Soma
May 2019
We show that -generically for diffeomorphisms of manifolds of dimension
, a homoclinic class containing saddles of different indices has a
residual subset where the orbit of any point has historic behavior.
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Apr 2019
Inspired by a recent work by Berger, we introduce the concept of pointwise
emergence. This concept provides with a new quantitative perspective into the
study of non-existence of averages for dynamical systems. We show that high
pointwise emergenc...
Nakano Yushi, Sakamoto Shota
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   39(4) 1779-1797   Apr 2019   [Refereed]
Kiriki Shin, Nakano Yushi, Soma Teruhiko
NONLINEARITY   32(3) 1111-1124   Mar 2019   [Refereed]
Yushi Nakano, Tomoo Yokoyama
Oct 2018
Since the pioneering work of Ghys, Langevin and Walczak among others, it has
been known that several methods of dynamical systems theory can be adopted to
study of foliations. Our aim in this paper is to investigate complexity of
foliations, by ge...
Yushi Nakano, Tomoo Yokoyama
Oct 2018
Since the pioneering work of Ghys, Langevin and Walczak among others, it has
been known that several methods of dynamical systems theory can be adopted to
study of foliations. Our aim in this paper is to investigate complexity of
foliations, by ge...
Yushi Nakano, Shota Sakamoto
Oct 2017
A typical approach to analysing statistical properties of expanding maps is
to show spectral gaps of associated transfer operators in adapted function
spaces. The classical function spaces for this purpose are Hölder spaces and
Sobolev spaces. N...
Nakano Yushi
TOKYO JOURNAL OF MATHEMATICS   40(1) 165-184   Jun 2017   [Refereed]

Takensは円周上の拡大写像について, 歴史的挙動を示すような初期値全体の集合が相空間上で残留的となることを示した. 本稿ではこの円周上の拡大写像の統計的性質が, 急冷型ランダム微小摂動によって保存されることを報告する. 証明はランダムなMarkov分割を構成することで得られるが, この分割の存在は(折畳み写像との位相共役に関する)ランダムな設定におけるShubの定理を示すことにより保証される. この副産物として, 円周上のランダム拡大写像の絶対連続でエルゴード的な不変確率測度に関する新...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Mar 2017
We consider a parametrised perturbation of a diffeomorphism on
a closed smooth Riemannian manifold with , modeled by nonautonomous
dynamical systems. A point without time averages for a (nonautonomous)
dynamical system is s...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Nonlinearity 30 (2017) 3255-3270   30(8) 3255-3270   Oct 2016   [Refereed]
We present a sufficient condition for three-dimensional diffeomorphisms
having heterodimensional cycles to be approximated arbitrarily well by
diffeomorphisms with non-trivial contracting wandering domains via several
perturbations. The key idea i...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Mar 2017
The point with no time averages for a random dynamical system is said to
have historic behaviour. It is known that for any absolutely continuous random
dynamical system of diffeomorphisms on a closed smooth
Riemannian manifold w...
Yushi Nakano, Masato Tsujii, Jens Wittsten
NONLINEARITY   29(7) 1917-1925   Nov 2015   [Refereed]
This paper concerns the compact group extension $f:\mathbb{T}^2\to \mathbb{T}^2,\quad f (x,s)= (E(x), s+\tau(x)\ \text{mod }1)$ of an expanding
map . The dynamics of and its stochastic
perturbations have pre...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Mar 2017
In this paper we consider a parametrised perturbation of a
diffeomorphism on a closed smooth Riemannian manifold with , modeled
by nonautonomous dynamical systems. A point without time averages for a
(nonautonomous) dynamic...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Oct 2016
We present a sufficient condition for three-dimensional diffeomorphisms
having heterodimensional cycles under which the diffeomorphisms can be
arbitrarily approximated by diffeomorphisms with non-trivial contracting
wandering domains. Moreover the...
Yushi Nakano
Stochastics and Dynamics   16(4)    Aug 2015   [Refereed]
We consider small perturbations of expanding maps induced by skew-product
mappings whose base dynamics are not invertible necessarily. Adopting a
previously developed perturbative spectral approach, we show stability of the
densities of the unique...
Yushi Nakano, Jens Wittsten
Nonlinearity 28 (2015) 951-1002   28(4) 951-1002   Apr 2014   [Refereed]
We consider quenched random perturbations of skew products of rotations on
the unit circle over uniformly expanding maps on the unit circle. It is known
that if the skew product satisfies a certain condition (shown to be generic in
the case of lin...
Yushi Nakano, Masato Tsujii, Jens Wittsten
Nonlinearity 29 (2016) 1917-1925   29(7) 1917-1925   Nov 2015
This paper concerns the compact group extension $f:\mathbb{T}^2\to \mathbb{T}^2,\quad f (x,s)= (E(x), s+\tau(x)\ \text{mod }1)$ of an expanding
map . The dynamics of and its stochastic
perturbations have pre...
Yushi Nakano
Tokyo Journal of Mathematics 40 (2017) 165-184      Oct 2015
Takens constructed a residual subset of the state space consisting of initial
points with historic behaviour for expanding maps on the circle. We prove that
this statistical property of expanding maps on the circle is preserved under
small random ...