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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 ...