Study of Complex Dynamical Systems of rational functions

1997年课题：3次、4次多项式映射和二次有理映射的模空间研究。特别是我们分析了双曲分量。并构造了单调分岔图的Nusse-Youke猜想的一个反例。(1)二次有理函数{mf(x)}m的非单调分岔，非线性分析，30,pp.1497 -1504;(2)多项式映射的模空间和对称轨迹，数学学报，pp.342 - 342;(3)具有两个临界点的映射的模空间，专刊号：1，中山大学科学通报，pp. 99 - 113, 1998年项目：4次多项式模空间的精细结构及其逃逸轨迹的研究。并给出了单调性猜想和反单调性猜想的两个例子。(1)一参数族的混沌分岔，Josai非线性分析，30,pp.1497 - 1504;(2)多项式映射的模空间和对称轨迹，ISSAC' 1997, pp.342 - 342;(3)四次多项式的两个仿射结构，专刊号：(4)一维地形图族的双向投叉分岔图，日本京都大学，《国学》第1期。1031(5)多项式映射的分支轨迹，日本京都大学。1042(6)具有非单调分岔图的1-参数1维族，日本京都大学学报，第1期。[10]代数曲线上的混沌分岔，1998年8月25 - 29日，波兰

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