Mathematical Sciences:NSF/CBMS Regional Conference in Mathematical Sciences-Complex Dynamics in Higher Dimensions; June 13-18, 1994; Albany, New York

9313042范围 约翰·E. Fornaess是多维复分析领域的国际领先专家，将提供一系列十个讲座，围绕复n维欧氏空间和射影空间的全纯自映射类的行为。 正如在一维的情况下-通过令人惊叹的计算机生成的可视化而广为人知-在更高维度中迭代这种映射揭示了令人惊讶的现象，以及需要理解的动力系统的新特性。 虽然第二维的一些工作可以追溯到20世纪20年代Fatou和Bieberbach的经典工作（Fatou和Julia一起是第一维复杂动力学的先驱之一），但Fornaess讲座中的大部分主题都是基于最近的工作。 该领域是目前许多调查的主题，有许多悬而未决的问题。 讲座的目的是使这一研究领域的非专家在多维复杂的分析，他们应该帮助数学家新的这一领域获得更深入的了解的主要问题和当前的研究方向，在这个新的和迅速扩大的研究领域。 会议将于1994年6月13日至18日在纽约州立大学奥尔巴尼大学校园举行。 奥尔巴尼是纽约州北部首都区的中心，是一个铸造地区，其中包括许多教育机构，奥尔巴尼大学，伦斯勒理工学院，联合学院，斯基德莫尔学院和锡耶纳学院。 多维复分析是奥尔巴尼大学的一个活跃的研究领域，许多经典函数论、遍历理论和（真实的）动力系统的专家都在该领域工作。 将作出特别努力，吸引来自邻近机构的感兴趣的参与者，他们可能想进入这一研究领域。 希望这一系列讲座将有助于建立来自该地区不同机构的数学家之间的新的互动，并刺激该地区多维复杂分析的新的研究努力。

9313042 Range Professor John E. Fornaess, a leading international expert in the area of multidimensional complex analysis, will present a series of ten lectures, centering around the behavior of classes of holomorphic self-maps of complex n- dimensional Euclidean spaces and projective spaces. Just as in the one dimensional case - widely known through stunning computer generated visualisations - iteration of such maps in higher dimensions reveals surprising phenomena, and new properties of dynamical systems which need to be understood. While some of the work in dimension two goes back to classical work of Fatou and Bieberbach in the 1920's (Fatou, together with Julia, is one of the pioneers of complex dynamics in dimension one), most of the topics covered in Fornaess' lectures are based on quite recent work. The field is the subject of many current investigations, and there are many open problems. The lectures are intended to make this research area accessible to non-experts in multidimensional complex analysis, and they should help mathematicians new to this field to gain a deeper understanding of the major problems and current directions of research in this new and rapidly expanding research area. The conference will take place June 13 to June 18, 1994, on the campus of the University of Albany, State University of New York. Albany is the center of the Capital District in Upstate New York, a cast region which includes among its many educational institutions the University of Albany, Rensselaer Polytechnic Institute, Union College, Skidmore College and Siena College. Multidimensional complex analysis is an active area of research at the University of Albany, and many experts in classical function theory, ergodic theory and (real) dynamical systems work in the region. A special effort will be made to attract interested participants from neighboring institutions, who may want to enter this research field. It is hoped that this series of lectures will help to build new interactions between mathematicians from the different institutions in the region, and stimulate new research efforts in multidimensional complex analysis in the region.