Study of Complex Dynamical Systems of rational functions

1997年项目：研究三次、四次多项式映射和二次有理映射的模空间。特别是对双曲分量进行了分析。(1)二次有理函数的非单调分支，《非线性分析》，30，第1497-1504页(2)多项式映射的模空间和对称轨迹，Issac‘97，第342-342页(3)具有两个临界点的映射的模空间，第1期，Josal大学科学公报。第99-113页1998项目：研究4次多项式的模空间的Alfine结构，并刻画逃逸轨迹。我们给出了两个单调性和反单调性猜想的例子：(1)单参数族的混沌分叉，Josai非线性分析，30,1497-1504页(2)模空间和多项式映射的对称轨迹，Issac‘97，第342-342页(3)施加在四次多项式中的两个仿射结构，第4期，Josai大学科学通报。第83-94(4)页一维地图族的双向叉叉分叉图，京东大学。多项式映射的Kokyu-Roku no.1031(5)分支轨迹，京东大学。Kokyu-Roku no.1042(6)1-参数一维非单调分岔图，京东大学。Kokyu-Roku No.1049国际会议分支和双曲分量，NACA98，新泻，1998年7月28-31日，沿代数曲线的混沌分支，ICDEA98，波兰，1998年8月25-29日

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 - 113Project 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. 1049International CongressBifurcations and hyperbolic components, NACA98, Niigata July 28 - 31 1998Chaotic bifurcations along algebraic curves, ICDEA98, Poland Aug 25 - 29 1998