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.

使用较早发展的诱导双曲性方法 由首席研究员，家庭的非线性动力学 系统将进行研究。 特别令人感兴趣的将是他们的 随机行为 单参数自同态族 在Feigenbaum不动点的不稳定流形附近， 接受检查。 沙利文的方法将用于 拓扑共轭蕴含拟共形性 具有绝对连续不变测度的映射的共轭性。 一个动力系统的不变测度是正的， 吸引或排斥系统的不变集。 的 首席研究员将研究这些系统， Feigenbaum极限的一些参数空间。 这种限制 倍周期分岔引起了人们的强烈兴趣， 研究人员在各种物理和生物 以理工科为重 一旦超过这个极限，混乱就开始了。