| Research Abstract |
Project of 1997 : Study of Moduli spaces for the polynomial maps with degree 3 and 4 and for the quadartic rational maps. Especially we analyzed hyperbolic components. And we construct a counter example to the Nusse-Youke's conjecture of monotonoe bifurcation diagrams.
(1) Non-monotone bifurcations for Quadratic rational functions {mf(x)}m, Nonlinear Analysis , 30, pp.1497 -1504
(2) Moduli spaces and and symmetry loci of polynomial maps, Proceedings of ISSAC'97, pp.342 - 342
(3) Moduli spaces of maps with two critical points, special issue no.1, Science Bulitin of Josal Univ. pp. 99 - 113
Project of 1998 : Study of alfine structure of the moduli sapce of the polynomials with degree 4, and characterize the escape locus. And we give two examples to the monotonicity and antinonotoniciyt conjectures.
(1) Chaotic bifurcation of one parameter family, Josai Nonlinear Analysis, 30, pp.1497 - 1504
(2) Moduli spaces and and symmetry loci of polynomial maps, Proceedings of ISSAC'97, pp.342 - 342
(3) Two affine structures imposed in the polynomials with degree four, Special issue no.4, Science Bulltin of Josai Univ. pp. 83 - 94
(4) Bothways pitch-fork bifurcation diagrams of family of one dimensional maps, Kyouto Univ. Kokyu-roku no.1031
(5) Branch locus of polynomial maps, Kyouto Univ. Kokyu-roku no. 1042
(6) 1-parmeter 1-dimensional family with non-monotone bifurcation diagram, Kyouto Univ. Kokyu-roku no. 1049
International Congress
Bifurcations and hyperbolic components, NACA98, Niigata July 28 - 31 1998
Chaotic bifurcations along algebraic curves, ICDEA98, Poland Aug 25 - 29 1998
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