Research on Complex Dynamics

上田研究了Fatou坐标（解决阿贝尔方程）抛物不动点和线性化函数（解决施罗德方程）吸引不动点复杂的解析函数的一个变量。他表明，法图坐标可以获得作为一个适当的限制线性化功能的序列地图的乘数趋于1。他还研究了全纯映射复杂的射影空间和特点的条件分析继续Fatou地图，这是一个广义的概念Fatou组件。Tsujii研究使用功能分析方法的遍历理论性质的（部分）双曲动力系统。对于某些二维部分双曲系统，他表明根据一般性假设，存在有限数量的措施理论吸引子和他们的盆地符合整个相空间模一套勒贝格措施零。他还研究了 ...更多信息 zeta函数的双曲动力系统及其解析延拓。在一个联合工作与志仓，猪研究了抛物重整化的一维复杂的动力系统。他们证明了抛物重整化的不变函数空间的存在性，这意味着它的扰动导致了非理性中立不动点的近抛物重整化的双曲性。作为应用，他们获得了小周期循环的乘数围绕非理性无关不动点的普遍行为。Buff和Cheritat也将上述结果作为关键步骤，证明了具有正Lebesgue测度的Julia集的二次多项式的存在性。这成为一个反例长期存在的问题，这是一个类比的阿尔福斯猜想合理的地图。在联合工作与志仓，木坂开发的技术quasiconformal手术，以显示存在的双重连接游荡域的超越整个职能。Ushiki可视化高维朱莉娅集。少

Ueda studied the Fatou coordinate (solution to Abel's equation) for parabolic fixed points and the linearization function (solution to Schroeder equation) for attracting fixed points for complex analytic functions of one variable. He showed that The Fatou coordinate can be obtained as an appropriate limit of the linearization functions for the sequence of maps whose multiplier tends to 1. He also studied holomorphic mappings on complex projective spaces and characterized the condition for the analytic continuation of Fatou maps, which is a generalized notion of Fatou components.Tsujii studied using functional analytic methods the ergodic theoretical properties of (partially) hyperbolic dynamical systems. For certain two dimensional partially hyperbolic systems, he showed under a genericity assumption that there exist a finite number of measure theoretic attractors and their basins coincide with the entire phase space modulo a set of Lebesgue measure zero. He also studied the dynamical … More zeta function for hyperbolic dynamical systems and its analytic continuation.In a joint work with Shishikura, Inou studied the parabolic renormalization of one dimensional complex dynamical systems. They showed the existence of an invariant space of function for the parabolic renormalization, and this implied that its perturbation leads to the hyperbolicity of the near-parabolic renormalization for irrationally indifferent fixed points. As an application they obtained the universal behavior of the multipliers of the small periodic cycles around irrationally indifferent fixed points. Buff and Cheritat also used the above result as a key step to show the existence of a quadratic polynomial with Julia set of positive Lebesgue measure. This became a counter-example to a long standing problem which is an analogy of Ahlfors conjecture for rational maps.In a joint work with Shishikura, Kisaka developed the technique of quasiconformal surgery to show the existence of doubly connected wandering domains for transcendental entire functions.Ushiki visualized higher dimensional Julia sets. Less