List of Publications


Preprints:

Conley index theory for fast-slow systems II: Multi-dimensional slow variable (with Tomas Gedeon, Hiroshi Kokubu, and Konstantin Mischaikow)


Papers:

[1] Existence d'attracteurs etranges dans le d'eploiement d'une singularite degeneree d'un champ de vecteuers invariant par translation, Comptes Rendus l'Academie des Sciences, Paris, Serie I, Mathematiques, t. 298 (1984), 39-42 (with Shigehiro Ushiki, Hiroshi Kokubu)

[2] Constrained Lorenz-like attractors, Japan Journal of Applied Mathematics, 2 (1985), 495-500 (with Hiroshi Kokubu)

[3] Normal forms for constrained equations and their applications to strange attractors, in "Proceedings of 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida", (1985), pp. 461-466 (with Hiroshi Kokubu)

[4] An approach to constrained equations and strange attractors, 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 (with Hiroshi Kokubu)

[5] Constrained system, characteristic surface and normal form, Japan Journal of Applied Mathematics, 4 (1987), 393-431.

[6] Versal unfoldings of constrained systems of corank 1, in "Proceedings of the International Conference on Bifurcation Theory and its Numerical Analysis, Xi'an, 1988" (Eds., L. Kaitai, J. Marsden, M. Golubitsky and G. Iooss), (1989), pp. 378-384, Xi'an Jiaotong University Press. (with Hiroshi Kokubu｡ﾋ

[7] Normal forms for constrained nonlinear differential equations - Part I: Theory, IEEE Transactions on Circuits and Systems, 35 (1988), 881-901 (with Leon O. Chua)

[8] Normal forms for constrained nonlinear differential equations - Part II: Bifurcation, IEEE Transactions on Circuits and Systems, 36 (1989), 71-88 (with Leon O. Chua)

[9] Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems, Journal of Differential Equations, 86 (1990), 260-341 (with Hiroshi Kokubu, Yasumasa Nishiura)

[10] Singular perturbation for certain types of ordinary differential equations and heteroclinic bifurcation, Proceedings of the International Symposium "Functional Differential Equations", (Eds. T. Yoshizawa and J. Kato), (1991), pp. 291-300, World Scientific.

[11] Supplement to homoclinic doubling bifurcation in vector fields, in "Dynamical Systems", (Eds. R. Bamon, R. Labarca, J. Lewowicz, and J. Palis, Jr.), Pitman Research Notes in Mathematics, Vol. 285, (1993), pp. 92-116, Longman Scientific and Technical (with Hiroshi Kokubu, Masashi Kisaka)

[12] Singular perturbations of autonomous ordinary differential equations and heteroclinic bifurcations, in "Dynamical Systems", (Eds. R. Bamon, R. Labarca, J. Lewowicz, and J. Palis, Jr.), Pitman Research Notes in Mathematics, Vol. 285, (1993), pp. 159-194, Longman Scientific and Technical.

[13] Bifurcations of N-homoclinic and N-periodic orbits in vector fields, Journal of Dynamics and Differential Equations, 5 (1993), 305-357 (with Hiroshi Kokubu, Masashi Kisaka)

[14] Bifurcation of Lorenz-like attractors from a degenerate vector field singularity, in "Towards the Harnessing of Chaos", (ed. M. Yamaguti), The Seventh TOYOTA Conference Procedings, (1994), pp. 389-392, Elsevier.

[15] A degenerate singularity generating geometric Lorenz attractors, Ergodic Theory and Dynamical Systems, 15 (1995), 833-856 (with Freddy Dumortier, Hiroshi Kokubu)

[16] Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equations, Nonlinearity, 9 (1996), 1263-1280 (with Hiroshi Kokubu, Konstantin Mischaikow)

[17] Multiple homoclinic bifurcations from orbit-flip, I: Successive homoclinic doublings, International Journal of Bifurcations and Chaos, 6 (1996), 833-850 (with Hiroshi Kokubu, Motomasa Komuro)

[18] Linear grading function and further reduction of normal forms, Journal of Differential Equations, 132 (1996), 293--318 (with Hiroshi Kokubu, Duo Wang)

[19] Connecting orbit structure of monotone solutions in the shadow system, Journal of Differential Equations, 140 (1997), 309-364 (with Hiroshi Kokubu, Konstantin Mischaikow, Yasumasa Nishiura, Takeshi Takaishi)

[20] Conley index for fast-slow systems I: One-dimensional slow variable, Journal of Dynamics and Differential Equations. Vol.11, 1999, pp427-470 (with Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, James Reineck)

[21] Directional transition matrix, in Proceedings of the Conley Index Theory (Eds. K. Mischaikow, M. Mrozek, P. Zgliczyynski), Banach Center Publication, Vol.47,1999, Warsaw, Polandpp133-144 (with Hiroshi Kokubu, Konstantin Mischaikow)

[22] Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing, Journal of Dynamics and Differential Equations, 14 (2002),63-84 (with Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow