KIRIKI Shin

J-GLOBAL         Last updated: Jun 5, 2019 at 15:54
 
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Name
KIRIKI Shin
Nickname
Shin Kiriki
Affiliation
Tokai University
Section
School of Science Department of Mathematics
Degree
修士(理学), Doctor of Science(Tokyo Denki University)

Research Areas

 
 

Academic & Professional Experience

 
2013
 - 
Today
Professor, Dept of Math., Tokai University
 
Feb 2017
 - 
Feb 2017
Visiting Researcher, Dept. Math., - Fluminense Federal University(Brazil)
 
2009
 - 
2013
Professor, Dept of Math., Kyoto University of Education
 
2005
 - 
2009
Associated professor, Dept of Math., Kyoto University of Education
 
Feb 2006
 - 
Mar 2006
Visiting Professor, Dept. Math., - NCTU (Taiwan)
 
Aug 2005
 - 
Sep 2005
Visiting Researcher, Inst. Math., - Academia Sinica (Taiwan)
 
2001
 - 
2005
lecturer with tenure, Dept. Math. Sci., Tokyo Denki University
 
1998
 - 
2001
research assistant(tenure), Dept. Math. Sci., Tokyo Denki University
 
1995
 - 
1998
non-tenure research assistant, Tokyo Denki University
 
Apr 1993
 - 
Apr 1995
Gust graduate student, Dept. Math., University of Groningen
 

Education

 
 
 - 
1995
数理科学, Graduate School, Division of Mathematical Sciences, Tokyo Denki University
 

Published Papers

 
Shin Kiriki, Yushi Nakano,Teruhiko Soma
Nonlinearity   32 1111-1124   Feb 2019   [Refereed]
Shinobu Hashimoto, Shin Kiriki, Teruhiko Soma
Discrete Contin. Dyn. Syst.   38(10) 5021-5037   Oct 2018   [Refereed]
We consider a space U of 3-dimensional diffeomorphisms f with hyperbolic fixed points p the stable and unstable manifolds of which have quadratic tangencies and satisfying some open conditions and such that Df(p) has non-real expanding eigenvalues...
Shin Kiriki, Yushi Nakano, Teruhiko Soma
Nonlinearity   30 3255-3270   Jul 2017   [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...
S. Kiriki & T. Soma
Adv. Math.   386 524-588   2017   [Refereed]
In this paper, we give an answer to a Cr
(2≤r<∞)
version of the open problem of Takens in [42] which is related to historic behavior of dynamical systems. To obtain the answer, we show the existence of non-trivial wandering domains near a homocli...
Shin Kiriki, Ming-Chia Li, Teruhiko Soma
Discrete Contin. Dyn. Syst.   36(12) 7021-7028   2016   [Refereed]
L. J. Díaz, Shin Kiriki, K. Shinohara
Nonlinearity   27 353-378   2014   [Refereed]
We give an explicit family of polynomial maps called center unstable
Hénon-like maps and prove that they exhibits blenders for some
parametervalues. Using this family, we also prove the occurrence of blenders
near certain non-transverse heterodi...
Ch. Bonatti, L. J. Díaz, Shin KIRIKI
Nonlinearity   25-4 (2012) 931–960    2012   [Refereed]
Shin KIRIKI, Teruhiko Soma
Ergodic Theory and Dynamical Systems   First published online 2012, see http://bit.ly/LCI88f    2012   [Refereed]
Shin Kiriki, Teruhiko Soma
   Sep 2011   [Refereed]
In this paper, we give sufficient conditions for the existence of Tex
robust heterodimensional tangency, and present a nonempty open set in
Tex with Tex each element of which has a non-degenerate
heterodimensional tangency...
Christian Bonatti, Lorenzo J. Diaz, Shin Kiriki
   Apr 2011   [Refereed]
We consider diffeomorphisms Tex with heteroclinic cycles associated to
saddles Tex and Tex of different indices. We say that a cycle of this type can
be stabilized if there are diffeomorphisms close to Tex with a robust cycle
associated to hyperbo...
KIRIKI Shin,LI Ming‐Chia,SOMA Teruhiko
Nonlinearity   23(9) 2253-2269   Sep 2010   [Refereed]
Shin Kiriki, Ming-Chia Li, Teruhiko Soma
   Jul 2010   [Refereed]
Let Tex be the (original) Hénon family. In this paper, we show
that, for any Tex near 0, there exists a closed interval Tex which contains
a dense subset Tex such that, for any Tex, Tex has a quadratic
homoclinic tange...
Blender structures for a non-normally Hénon-like family
Shin Kiriki & Masaki Nakajima
Tamkang Jour. Math.   42-2    2010   [Refereed]
Shin Kiriki, Yusuke Nishizawa, Teruhiko Soma
Discrete and Continuous Dynamical Systems - Series A   27-1, 285-300    2010   [Refereed]
Shin Kiriki, Teruhiko Soma
Nonlinearity 21 (2008) 1105-1140   23-9 (2010) 2253–2269(9) 2253-2269   Mar 2008   [Refereed]
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 dissipative saddle point. Our first
theorem presents an open set in the...
Shin KIRIKI, Teruhiko Soma
Dynamical Systems an International Journal   22-4 (2007), 1--13    2007   [Refereed]
Shin Kiriki, Teruhiko Soma
   Aug 2006   [Refereed]
In this paper, we show that the Hénon map Tex has a generically
unfolding cubic tangency for some Tex arbitrarily close to Tex by
applying results of Gonchenko-Shilnikov-Turaev [12]-[16]. Combining this fact
with theorems in...
KIRIKI Shin,SOMA Teruhiko
東京電機大学総合研究所年報   (25) 257-260   Aug 2006   [Refereed]
Shin KIRIKI, Teruhiko Soma
Trans. Amer. Math. Soc.   357 (2005), 1325-1339    2005   [Refereed]
Annual report   25, 257~260(25) 257-260   2005
Forward limit sets of singularities for the Lozi family
Shin KIRIKI
Hokkaido Math. Jour.   33 (2004), 491-510    2004   [Refereed]
Shin Kiriki, Teruhiko Soma
   Dec 2003   [Refereed]
In this paper, we will show that any geometric Lorenz flow in a definite
class satisfies the parameter-shifted shadowing property.
Shin KIRIKI, Yongluo Cao
Chaos Solitons Fractals   13 (2002), 665--671.    2002
Parameter-shifted shadowing property and stochastic stability of Lozi maps
Shin KIRIKI
ICM Satellite Conf. New Directions in Dynamical Systems   309    2002
Annual report   (22) 185-196   2002
Shin KIRIKI, Yongluo Cao
Chaos Solitons and Fractals   11(5) 729-734   2000
An isolated saddle-node bifurcation occurring inside a horseshoe
Shin Kiriki
Dynam. Stability Systems   15 (2000) no. 1, 1--20.    2000
Kiriki Shin, Nakajima Masaki
RIMS Kokyuroku   1072 91-102   Dec 1998
Yongluo Cao, Shin Kiriki
   Oct 1998
In this paper, we consider a smooth arc of diffeomorphisms which has a
saddle-node bifurcation inside a nontrivial invariant set which is a
deformation of a horseshoe. We show that this saddle-node bifurcation is
isolated, that is, its hyperbolici...
Research announcements of a mult-dimeusionul Henon family
Shin KIRIKI, Masaki Nakajima
Res. Act. Fac. Sci. Engrg. Tokyo Denki Univ   20, no. 1, 15--20.    1998
Shin KIRIKI
Internat. J. Bifur. Chaos Appl. Sci. Engrg.   6, no. 4, p. 737--744.    1996
Hyperbolicity of the Special 1-parameter Family with a First Homoclinic Tangency
Shin KIRIKI
Dynamics and Stability of Systems   11, no. 1, p.3--18.    1996
Classification of the heteroclinic Ω-explosion in Chaotic Dynamical System
Shin KIRIKI
Proceeding of the RIMS   No. 814, 94--111.    1994
Kiriki Shin
RIMS Kokyuroku   814 94-111   Nov 1992

Misc

 
Pablo G. Barrientos, Shin Kiriki, Yushi Nakano, Artem Raibekas, Teruhiko Soma
   May 2019
We show that Tex-generically for diffeomorphisms of manifolds of dimension
Tex, 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...
KIRIKI SHIN
Bussei Kenkyu   66(4) 807-814   Jul 1996
We introduce a general definition of first homoclinic tangency, and construct a 1-parameter family of planar diffeomorphisms from Smale's n-fold horseshoe diffeomorphism, which has the first homoclinic tangency that is a first bifurcation introduc...

Research Grants & Projects

 
Heterodimensional tangencies on cycles leading to strange attractors
Grant-in-Aid for Scientific Research
Project Year: 2008 - 2010
See:
Heterodimensional tangencies on cycles leading to strange attractors (col- laboration with Y. Nishizawa & T. Soma), Discrete Contin. Dyn. Syst. 27-1 (2010) 285–300
Coexistence of homoclinic sets with and without SRB measures in Hénon family
The Other Research Programs
Project Year: 2008 - 2010
See:
Coexistence of homoclinic sets with and without SRB measures in Hénon family (collaboration with M.-C. Li and T. Soma), Nonlinearity 23-9 (2010) 2253–2269
Stabilization of heterodimensional cycles
Grant-in-Aid for Scientific Research
Project Year: 2010 - 2012
See: Stabilization of heterodimensional cycles (collaboration with Ch. Bonatti & L.J. Díaz), Nonlinearity 25-4 (2012) 931–960
C^2-ROBUST HETERODIMENSIONAL TANGENCIES
Grant-in-Aid for Scientific Research
Project Year: 2010 - 2012
In this research, we give sufficient conditions for the existence of C^2 robust heterodimensional tangency, and present a nonempty open set in Diff^2(M) each element of which has a non-degenerate heterodimensional tangency on a C^2 robust heterodi...
Non-connected bifurcating cycles between equidimension and heterodimension
The Other Research Programs
Project Year: 2008 - 2010
See:
Blender structures for a non-normally H ́eon-like family, (collaboration with M. Nakajima), Tamkang Jour. Math. 42-2 (2010),