Mathematical Sciences: The Method of Induced Hyperbolicity for One-Dimensional Maps and Two-Dimensional Diffeomorphisms

数学科学：一维映射和二维微分同胚的诱导双曲性方法

• 批准号: 9001631
• 负责人: Michael Jakobson
• 金额: $ 5.95万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-01 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001631&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Method; Induced; Hyperbolicity

Using the method of induced hyperbolicity developed earlier by the principal investigator, families of nonlinear dynamical systems will be studied. Of particular interest will be their stochastic behavior. One-parameter families of diffeomorphisms close to the unstable manifold of the Feigenbaum fixed point will be inspected. And Sullivan's approach will be used to investigate when topological conjugacy implies quasiconformal conjugacy for maps with absolutely continuous invariant measures. An invariant measure of a dynamical system is positive on invariant sets of the system which attract or repel. The principal investigator will study such systems which are close in some parameter space to the Feigenbaum limit. This limit of period-doubling bifurcations has raised intense interest from investigators in a wide variety of physical and biological sciences. Just past this limit lies the onset of chaos.

使用主要研究者早期开发的诱导双曲线方法，将研究非线性动力学系统的家族。 特别感兴趣的是他们的随机行为。 将检查接近Feigenbaum固定点不稳定多种流形的差异性的一个参数家族。 Sullivan的方法将用于调查何时拓扑结合段暗示具有绝对连续不变措施的地图的准信息共轭。 动态系统的不变度量是吸引或排斥系统的不变集合。 首席研究人员将研究这些系统在某些参数空间接近Feigenbaum限制的系统。 这种倍增分叉的限制使研究人员在各种物理和生物学科学方面提高了浓厚的兴趣。 刚刚超过了这个限制，这是混乱的发作。