62 citations · 211 across the 28 of their papers we have counts for
21 papers · 1 filter
-robust strong pluripotency for blender-horseshoes
Teruhiko Soma, Shuntaro Tomizawa
Suppose that is a closed manifold of dimension greater than two. We show that there exists a -diffeomorphism with a wild affine blender-horseshoe…
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 \(C^r\)-diffeomorphism \(f:M\to M\) with a wild affine blender-horses…
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…
Takens' Last Problem and strong pluripotency
Shin Kiriki, Xiaolong Li, Yushi Nakano +2
We consider the concept of strong pluripotency of dynamical systems for a hyperbolic invariant set, as introduced in [KNS]. To the best of our knowledge, for the whole hyperbolic i…
Pluripotency of wandering dynamics
Shin Kiriki, Yushi Nakano, Teruhiko Soma
This paper isolates a perturbative mechanism, which we call \emph{pluripotency}, by which the symbolic and statistical behavior of prescribed orbits in a uniformly hyperbolic set c…
Observable Lyapunov irregular sets for planar piecewise expanding maps
Yushi Nakano, Teruhiko Soma, Kodai Yamamoto
For any integer with , we present a one-parameter family of 2-dimensional piecewise expanding maps such that each has an ob…
Abundance of observable Lyapunov irregular sets
Shin Kiriki, Xiaolong Li, Yushi Nakano +1
Lyapunov exponent is widely used in natural science to find chaotic signal, but its existence is seldom discussed. In the present paper, we consider the problem of whether the set…
Historic and physical wandering domains for wild blender-horseshoes
Shin Kiriki, Yushi Nakano, Teruhiko Soma
We present diffeomorphisms of wild blender-horseshoes which belong to closures of two types of diffeomorphisms, one of which has a historic contracting wan…
Historic behavior in non-hyperbolic homoclinic classes
Pablo G. Barrientos, Shin Kiriki, Yushi Nakano +2
We show that -generically for diffeomorphisms of manifolds of dimension , a homoclinic class containing saddles of different indices has a residual subset where the or…
Emergence via non-existence of averages
Shin Kiriki, Yushi Nakano, Teruhiko Soma
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 a…
Moduli of 3-dimensional diffeomorphisms with saddle-foci
Shinobu Hashimoto, Shin Kiriki, Teruhiko Soma
We consider a space of 3-dimensional diffeomorphisms with hyperbolic fixed points the stable and unstable manifolds of which have quadratic tangencies and sat…
Historic behaviour for nonautonomous contraction mappings
Shin Kiriki, Yushi Nakano, Teruhiko Soma
We consider a parametrised perturbation of a diffeomorphism on a closed smooth Riemannian manifold with , modeled by nonautonomous dynamical systems. A poin…
Non-trivial wandering domains for heterodimensional cycles
Shin Kiriki, Yushi Nakano, Teruhiko Soma
We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial cont…
Geometric Lorenz flows with historic behavior
Shin Kiriki, Ming-Chia Li, Teruhiko Soma
We will show that, in the the geometric Lorenz flow, the set of initial states which give rise to orbits with historic behavior is residual in a trapping region.
Takens' last problem and existence of non-trivial wandering domains
Shin Kiriki, Teruhiko Soma
In this paper, we give an answer to a version of the open problem of Takens in [Nonlinearity, 21 (2008), no.3, T33-T36] which is related to historic beh…
-robust heterodimensional tangencies
Shin Kiriki, Teruhiko Soma
In this paper, we give sufficient conditions for the existence of robust heterodimensional tangency, and present a nonempty open set in $\Diff^2(M)$ with ea…
Coexistence of invariant sets with and without SRB measures in Hénon family
Shin Kiriki, Ming-Chia Li, Teruhiko Soma
Let be the (original) Hénon family. In this paper, we show that, for any near , there exists a closed interval which contains a dense subset such th…
Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies
Shin Kiriki, Teruhiko Soma
In this paper, we study a two-parameter family of two-dimensional diffeomorphisms such that it has a cubic homoclinic tangency unfolding generically which is associated with a diss…
Heterodimensional tangencies on cycles leading to strange attractors
Shin Kiriki, Yusuke Nishizawa, Teruhiko Soma
In this paper, we study heterodimensional cycles of two-parameter families of 3-dimensional diffeomorphisms some element of which contains nondegenerate heterodimensional tangencie…
Existence of generic cubic homoclinic tangencies for Hénon maps
Shin Kiriki, Teruhiko Soma
In this paper, we show that the Hénon map has a generically unfolding cubic tangency for some arbitrarily close to by applying results of Gonchenko-Shiln…
Parameter-shifted shadowing property for geometric Lorenz attractors
Shin Kiriki, Teruhiko Soma
In this paper, we will show that any geometric Lorenz flow in a definite class satisfies the parameter-shifted shadowing property.