Hiroshi Kokubu

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Hiroshi Kokubu

Published Papers

 
Existence d'attracteurs etranges dans le deploiement d'une singularite degeneree d'un champ de vecteuers invariant par translation
Shigehiro Ushiki, Hiroe Oka, and Hiroshi Kokubu
Comptes Rendus l'Academie des Science, Paris, Serie I, Mathematiques,298,39-42   298 39-42   1984   [Refereed]
H. Kokubu
Japan Journal of Applied Mathematics   1(2) 273-297   1984   [Refereed]
H. Oka and H. Kokubu
Japan Journal of Applied Mathematics   2(2) 495-500   1985   [Refereed]
An approach to constrained equations and strange attractors,
Hiroe Oka and Hiroshi Kokubu
in "Patterns and Waves - Qualitative Analysis of Nonlinear Differential Equations'',   (Eds. H. Fujii, M. Mimura and T. Nishida), Stud. Math. Appl., Vol. 18, (1986), pp. 607-630, Kinokuniya/North-Holland.      1986   [Refereed]
H. Kokubu
Japan Journal of Applied Mathematics   5(3) 455-501   1988   [Refereed]
Leon O. Chua and Hiroshi Kokubu
IEEE Transactions on Circuits and Systems   35(7) 863-880   1988   [Refereed]
Normal forms for nonlinear vector fields, Part II: Bifurcation
Leon O. Chua and Hiroshi Kokubu
IEEE Transactions on Circuits and Systems   36 51-70   1989   [Refereed]
H. Kokubu, Y. Nishiura, and H. Oka
Journal of Differential Equations   86(2) 260-341   1990   [Refereed]
H. Kokubu
ZAMP Zeitschrift für angewandte Mathematik und Physik   44(3) 510-536   1993   [Refereed]
M. Kisaka, H. Kokubu, and H. Oka
Journal of Dynamics and Differential Equations   5(2) 305-357   1993   [Refereed]
Supplement to homoclinic doubling bifurcation in vector fields
Masashi Kisaka, Hiroshi Kokubu, and Hiroe Oka
in "Dynamical Systems", (Eds. R. Bamon, R. Labarca, J. Lewowicz, and J. Palis, Jr.), Pitman Research Notes in Mathematics,   258 92-116   1993   [Refereed]
The cusp horseshoe and its bifurcations from inclination-flip homoclinic orbits
Ale Jan Homburg, Hiroshi Kokubu, and Martin Krupa
Ergodic Theory and Dynamical Systems   14 667-693   1994   [Refereed]
A degenerate singularity generating geometric Lorenz attractors
F. Dumortier, H. Kokubu, and H. Oka
Ergodic Theory and Dynamical Systems   15 833-856   Oct 1995   [Refereed]
H. Kokubu; M. Komuro; H. Oka
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering   6(5) 833-850   May 1996   [Refereed]
H. Kokubu; K. Mischaikow; H. Oka
Nonlinearity   9(5) 1263-1280   Sep 1996   [Refereed]
Kokubu, H; Oka, H; Wang, D
JOURNAL OF DIFFERENTIAL EQUATIONS   132(2) 293-318   Dec 1996   [Refereed]
The existence of infinitely many homoclinic doubling bifurcations from some codimension 3 homoclinic orbits
H. Kokubu; V. Naudot
Journal of Dynamics and Differential Equations   9(3) 445-462   1997   [Refereed]
H. Kokubu; K. Mischaikow; Y. Nishiura; H. Oka; T. Takaishi
Journal of Differential Equations   140(2) 309-364   Nov 1997   [Refereed]
The Conley index for fast-slow systems I. One-dimensional slow variable
T. Gedeon; H. Kokubu; K. Mischaikow; H. Oka; J.F. Reineck
Journal of Dynamics and Differential Equations   11(3) 427-470   1999   [Refereed]
Directional transition matrix
Hiroshi Kokubu, Konstantin Mischaikow, and Hiroe Oka
   1999   [Refereed]
F. Dumortier; H. Kokubu
Ergodic Theory and Dynamical Systems   20 85-107   Feb 2000   [Refereed]
F. Dumortier; S. Ibáñez; H. Kokubu
Dynamical Systems   16(1) 63-95   Mar 2001   [Refereed]
Homoclinic-doubling cascades
Homburg, AJ; Kokubu, H; Naudot, V
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   160(3) 195-243   Nov 2001   [Refereed]
Chaotic Solutions in Slowly Varying Perturbations of Hamiltonian Systems with Applications to Shallow Water Sloshing
T. Gedeon; H. Kokubu; K. Mischaikow; H. Oka
Journal of Dynamics and Differential Equations   14(1) 63-84   2002   [Refereed]
Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences, Part I
Hiroshi Kokubu and Robert Roussarie
Journal of Dynamics and Differential Equations, 16, 513-557      2004   [Refereed]
F. Dumortier; S. Ibáñez; H. Kokubu
Nonlinearity   19(2) 305-328   Feb 2006   [Refereed]
T. Gedeon; H. Kokubu; K. Mischaikow; H. Oka
Journal of Differential Equations   225(1) 242-307   Jun 2006   [Refereed]
M. Gameiro; T. Gedeon; W. Kalies; H. Kokubu; K. Mischaikow; H. Oka
Journal of Dynamics and Differential Equations   19(3) 623-654   Sep 2007   [Refereed]
Kokubu, Hiroshi; Wilczak, Daniel; Zgliczynski, Piotr
NONLINEARITY   20(9) 2147-2174   Sep 2007   [Refereed]
S. Day; H. Kokubu; S. Luzzatto; K. Mischaikow; H. Oka; P. Pilarczyk
Nonlinearity   21(9) 1967-1987   Sep 2008   [Refereed]
Z. Arai; W. Kalies; H. Kokubu; K. Mischaikow; H. Oka; P. Pilarczyk
SIAM Journal on Applied Dynamical Systems   8(3) 757-789   2009   [Refereed]
Recent development in rigorous computational methods in dynamical systems
Z. Arai; H. Kokubu; P. Pilarczyk
Japan Journal of Industrial and Applied Mathematics   26(2-3) 393-417   Oct 2009   [Refereed]
Topological bifurcation theorems for Morse decompositions
Hiroshi Kokubu
「Far-From-Equiiibrium Dynamics」、1 月8 日( 土)      2011   [Refereed]
H. Kokubu; K. Mischaikow
Procedia IUTAM   5 195-198   2012   [Refereed]
J. Bush; M. Gameiro; S. Harker; H. Kokubu; K. Mischaikow; I. Obayashi; P. Pilarczyk
Chaos   22(4)    2012   [Refereed]
F. Dumortier; S. Ibañez; H. Kokubu; C. Simó
Discrete and Continuous Dynamical Systems- Series A   33(10) 4435-4471   2013   [Refereed]

Misc

 
ON A CODIMENSION-2 BIFURCATION OF HETEROCLINIC ORBITS
KOKUBU, H
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   63(8) 298-301   Oct 1987   [Refereed]
Heteroclinic bifurcations associated with different saddle indices
Hiroshi Kokubu
in Proceedings of the International Conference "Dynamical Systems and Related Topics" (Ed. K. Shiraiwa), Advanced Series in Dynamical Systems, Vol. 9, pp. 236-260, World Scientific.      1991   [Refereed]
On transition matrices
Hiroshi Kokubu
EQUADIFF99, Proceedings of the International Conference on Differential Equations, Berlin, Germany 1-7 August 1999, World Scientific      2000   [Refereed]
Z. Aral; W. Kalies; H. Kokubu; K. Mischaikow; H. Oka; P. Pilarczyk
AIP Conference Proceedings   1168 918-921   2009   [Refereed]

Books etc

 
Bifurcations - Sights, Sounds and Mathematics
Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu, and Ryuji Tokunaga
Springer-Verlag,   1993   
カオス力学系入門 第2版
ロバート・L. ドゥヴェイニー,Robert L. Devaney,後藤 憲一,石井 豊,木坂 正史,国府 寛司,新居 俊作
共立出版   Nov 2003