All articles are given by PDF files.


Preprints

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.
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

  1. 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.
  2. Rigidity of certain solvable actions on the torus, Geometry, Dynamics, and Foliations 2013, Adv. Stud. Pure Math. 72, 269-281.
  3. (with K.Irie) A C^\infty closing lemma for Hamiltonian diffeomorphisms of closed surfaces, GAFA 26 (2016) no.5, 1245-1254.
  4. (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.
  5. (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.
  6. Local rigidity of homogeoenous actions of parabolic subgroups of rank-one Lie groups. J. Modern Dynamics 9 (2015), 191-201.
  7. (with K. Yamamoto) On the large deviation rates on non-entropy-approachable measure. Disc. and Conti. Dyn. Sys. 33 (2013), no. 10, 4401-4410.
  8. Rigidity of certain solvable actions on the sphere. Geom. and Topology 16 (2012), no. 3, 1835-1857.
  9. (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.
  10. Non-homogeneous locally free actions of the affine group. Ann. of Math. 175 (2012), no.1, 1-21.
  11. (with T.Fukaya, M.Tsumakoto) Remark on dynamical Morse inequality. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011) no. 9, 178-182.
  12. Regular projectively Anosov flows on three dimensional manifolds. Ann. Inst. Fourier, 60 (2010) no. 5, p. 1649-1684.
  13. On Invariant volumes of codimension-one Anosov flows and the Verjovsky conjecture. Invent. Math., 174 (2008), no. 2, 435 - 462. and Erratum
  14. Hyperboic sets exhibiting $C^1$-persistent homoclonic tangency for higher dimensions. Proc. A.M.S. 136 (2008), no. 2,677-686. and Erratum
  15. Invariants of two dimensional projectively Anosov diffeomorphisms and their appliacations. J. Math. Japan. Soc., 59 (2007) no.3, 603-649.
  16. 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.
  17. Codimension-one foliations with a transversely contracting flow. Foliations 2005, 21--36, World Sci. Publ., Hackensack, NJ, 2006.
  18. Classification of regular and non-degenerate projectively Anosov flows on three dimensional manifolds. J. Math. Kyoto Univ. 46 (2006), no.2, 349-356.
  19. A classification of three dimensional regular projectively Anosov flows. Proc. Japan. Acad. Ser. A. 80 (2004), no.10, 194-197.
  20. Invariants of two dimensional projectively Anosov diffeomorphisms. Proc. Japan. Acad. Ser. A. 78 (2002), no.8, 161-165.
  21. Area preserving monotone twist diffeomorphisms without non-Birkhoff periodic points. J. Math. Kyoto. Univ. 42 (2002), no.4, 703-714.
  22. Markov covers and finiteness of periodic attractors for diffeomorphisms with a dominated splitting. Ergod. Th. & Dyn. Sys. 20 (2000), no.1, 1-14.
  23. 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

  1. Rigidity and deformation of smooth group actions (slides) (Japanese)
    The 58th Geometry Symposium, Yamaguchi University, Japan, 2011.
  2. Parameter rigidity and leafwise cohomology (slides)
    Geometry and Analysis, Kyoto University, Japan, 2011.
  3. 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.
  4. Local rigidity of homogeneous actions of parabolic subgroups of Lie groups of real-rank one (Japanese)
    Autumn Meeting of MSJ, Osaka University, Japan, 2009.
  5. Rigidity and Flexibility of codimension-one actions of solvable groups (Japanese)
    Spring Meeting of MSJ, Kinki University, Japan, 2008.
  6. Deformation of dynamical systems and statistical mechanics (slides) (Japanese)
    Kinosaki Freshman Seminar, Kinosaki, Japan, 2008.
  7. On rigidity of codimension-one actions of solvable Lie groups (Japanese)
    Abstract for Topology symposium 2007, Aizu University, Aizu-Wakamatsu, Japan.
  8. 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.)
  9. Invariants of 2-dimensional projectively Anosov diffeomorphisms and thier applications (Japanese)
    Abstract for Topology symposium 2002, Okinawa seinenkaikan, Naha, Japan.
  10. 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