Studies on global bifurcations for dynamical systems

1.非双曲动力系统的研究，特别是针对Palis猜想的一个结果，该猜想旨在描述C^1拓扑(Hayashi)中稠密动力系统的动力结构。2.与遍历理论有关的复杂动力系统和超函数，特别是Ruelle算子(Ushiki)3.二维实解析和高维分段线性扩展映射中绝对连续不变测度的存在性和统计性质(Tsujii)4.一维慢动力学情形下慢-快型奇异摄动向量场的Conley指数理论(Oka)5.分段线性对称双峰映射拓扑熵的单调性(Oka)6.Rayleigh-Benard问题中整体分支现象的解析和计算机辅助方法，特别是用有效的数值计算证明各种不同参数的解的存在性的新方法(西田和吉原)7.Proudman-Johnson方程解的爆破(Okamoto)8.描述在真实的化学和生物实验中观察到的新的空间模式的自复制模式的分析和动力学研究(Nishiura)

The following results have been obtained in this research project :1. Study of non-hyperbolic dynamical systems, in particular, a result toward Palis conjecture that aims at describing dynamical structures for a dense set of dynamical systems in C^1 topology (Hayashi)2. Complex dynamical systems and hyper functions in relation to ergodic theory, in particular the Ruelle operator (Ushiki)3. Existence and statistical properties of absolutely continuous invariant measures in two dimensional real analytic and higher dimensional piecewise linear expanding maps (Tsujii)4. Conley index theory for singularly perturbed vector fields of slow-fast type in the case of one-dimensional slow dynamics (Oka)5. Monotonicity of topological entropy for piecewise-linear symmetric bimodal maps (Oka)6. Analytic and computer assisted approach to global bifurcation phenomena in the Rayleigh-Benard problem, in particular a new method for proving the existence of solutions for various different parametres using the validated numerical computation (Nishida and Yoshihara)7. Blow-up of solutions in the Proudman-Johnson equation (Okamoto)8. Analytical and dynamical investigation of self-replicating patterns which describe new spatial patterns observed in real chemical and biological experiments (Nishiura)