All articles are given by PDF files.
Preprints
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C^1 stable intersection of Cantor sets and its applications.
- In this paper, we give a criterion that
two regular Cantor sets in higher dimensions have
C1-stable intersection and provide a concrete example
which satisfies the condition.
This contrasts that no regular Cantors sets in the real line
have C1-stable intersection.
As an application of the criterion, we construct a hyperbolic basic set
which exhibits C2-robust homoclinic tangency of the largest codimension
for any higher dimensional manifold.
This answers a question posed by Barrientos and A.Raibekas.
- (with K.Shinohara, D.Turaev)
Fast growth of the number of periodic points arising
from heterodimensional connections,
arXiv:1808.07218.
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We consider C^r-diffeomorphisms of a compact smooth manifold
having a pair of robust heterodimensional cycles
where r is a positive integer or infinity.
We prove that if certain conditions about
the signatures of non-linearities and Schwarzian derivatives
of the transition maps are satisfied,
then by giving C^r arbitrarily small perturbation,
we can produce a periodic point at which the first return map
in the center direction is C^r-flat.
As a consequence, we will prove that C^r-generic diffeomorphisms
in the neighborhood of the initial diffeomorphism exhibit
super-exponential growth of number of periodic points.
We also give examples which show the necessity of the conditions
on non-linearities and the Schwarzian derivatives.
Published papers
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Abundance of fast growth of the number of periodic points
in 2-dimensional area-preserving dynamics,
Comm. Math. Phys. 356 (2017), no. 1, 1-17.
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Rigidity of certain solvable actions on the torus,
Geometry, Dynamics, and Foliations 2013,
Adv. Stud. Pure Math. 72, 269-281.
-
(with K.Irie)
A C^\infty closing lemma for Hamiltonian diffeomorphisms
of closed surfaces,
GAFA 26 (2016) no.5, 1245-1254.
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(with K.Shinohara, D.Turaev)
Degenerate behavior in non-hyperbolic semigroup actions on the interval:
fast growth of periodic points and universal dynamics
Math. Ann. 368 (2016) no.3-4, 1277-1309.
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(With T.Fukaya, K.Mitsui, and M. Tsukamoto)
Growth of critical points in one-dimensional lattice systems.
J.d'Analyse Mathematique 127 (2015) no. 1, 47-68.
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Local rigidity of homogeoenous actions of parabolic subgroups
of rank-one Lie groups.
J. Modern Dynamics 9 (2015), 191-201.
-
(with K. Yamamoto)
On the large deviation rates on non-entropy-approachable measure.
Disc. and Conti. Dyn. Sys. 33 (2013), no. 10, 4401-4410.
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Rigidity of certain solvable actions on the sphere.
Geom. and Topology 16 (2012), no. 3, 1835-1857.
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(with E. Dufraine and T. Noda)
Homotopy classes of total foliations
and bi-contact structures on three-manifolds.
Comm. Math. Helv. 87 (2012), no. 2, 271-302.
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Non-homogeneous locally free actions of the affine group.
Ann. of Math. 175 (2012), no.1, 1-21.
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(with T.Fukaya, M.Tsumakoto)
Remark on dynamical Morse inequality.
Proc. Japan Acad. Ser. A Math. Sci.
87 (2011) no. 9, 178-182.
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Regular projectively Anosov flows on three dimensional manifolds.
Ann. Inst. Fourier, 60 (2010) no. 5, p. 1649-1684.
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On Invariant volumes of codimension-one Anosov flows
and the Verjovsky conjecture.
Invent. Math.,
174 (2008), no. 2, 435 - 462.
and Erratum
-
Hyperboic sets exhibiting $C^1$-persistent
homoclonic tangency for higher dimensions.
Proc. A.M.S.
136 (2008), no. 2,677-686.
and Erratum
-
Invariants of two dimensional projectively Anosov diffeomorphisms
and their appliacations.
J. Math. Japan. Soc.,
59 (2007) no.3, 603-649.
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On Reeb components of invariant foliations
of projectively Anosov flows.
Top. and its Appl. (Special Issue: The Third Joint Meeting Japan-Mexico
in Topology and its Applications)
154 (2007), no.7, 1263-1268.
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Codimension-one foliations with a transversely contracting flow.
Foliations 2005, 21--36,
World Sci. Publ., Hackensack, NJ, 2006.
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Classification of regular and non-degenerate projectively Anosov flows
on three dimensional manifolds.
J. Math. Kyoto Univ. 46 (2006), no.2, 349-356.
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A classification of three dimensional regular projectively Anosov flows.
Proc. Japan. Acad. Ser. A. 80 (2004), no.10, 194-197.
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Invariants of two dimensional projectively Anosov diffeomorphisms.
Proc. Japan. Acad. Ser. A. 78 (2002), no.8, 161-165.
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Area preserving monotone twist diffeomorphisms
without non-Birkhoff periodic points.
J. Math. Kyoto. Univ. 42 (2002), no.4, 703-714.
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Markov covers and finiteness of periodic attractors
for diffeomorphisms with a dominated splitting.
Ergod. Th. & Dyn. Sys. 20 (2000), no.1, 1-14.
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A natural horseshoe-breaking family
which has a period doubling bifurcation as the first bifurcation.
J. Math. Kyoto. Univ. 37 (1997), 493-511.
Reviews on MathSciNet
Other articles / Slides
-
Rigidity and deformation of smooth group actions
(slides) (Japanese)
The 58th Geometry Symposium, Yamaguchi University, Japan, 2011.
- Parameter rigidity and leafwise cohomology
(slides)
Geometry and Analysis, Kyoto University, Japan, 2011.
- Deformation of locally free actions and the leafwise cohomology
(arXiv:math/1012.2946)
An expanded version of the lecture note of my lectures
at "Advanced courses in Foliation",
which was held at the Centre de Recerca Mathematica in the May of 2010.
- Local rigidity of homogeneous actions
of parabolic subgroups of Lie groups of real-rank one
(Japanese)
Autumn Meeting of MSJ, Osaka University, Japan, 2009.
-
Rigidity and Flexibility of codimension-one actions of solvable groups
(Japanese)
Spring Meeting of MSJ, Kinki University, Japan, 2008.
- Deformation of dynamical systems
and statistical mechanics (slides)
(Japanese)
Kinosaki Freshman Seminar, Kinosaki, Japan, 2008.
-
On rigidity of codimension-one actions of solvable Lie groups
(Japanese)
Abstract for Topology symposium 2007,
Aizu University, Aizu-Wakamatsu, Japan.
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On Kaloshin's works about Artin-Mazur maps (Japanese)
A Lecture note for Seminar on Dynamical Systems 2004,
Hokkaido University, Sapporo, Japan. (2004/09/30 2nd ed.)
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Invariants of 2-dimensional projectively Anosov diffeomorphisms
and thier applications (Japanese)
Abstract for Topology symposium 2002,
Okinawa seinenkaikan, Naha, Japan.
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An invariant for projectively Anosov diffeomorphisms
on the two-dimensional torus,
New developments in dynamical systems,
Proceedings of a symposium held at
the Research Institute for Mathematical Sciences,
Kyoto University, Kyoto, September 18--22,
Suurikaiseki Kenkyujo Koukyuroku
1179 (2000), 94-98.
e-mail: asaokaQmath.kyoto-u.ac.jp (replace "Q" to "@")
Masayuki ASAOKA|
Department of Mathematics|
Kyoto University