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.

使用首席研究员早期开发的诱导双曲性方法，将研究非线性动力系统族。 特别令人感兴趣的是它们的随机行为。 将检查接近费根鲍姆不动点不稳定流形的单参数微分同胚族。 沙利文的方法将用于研究拓扑共轭何时意味着具有绝对连续不变测度的映射的拟共形共轭。 动力系统的不变测度对于吸引或排斥的系统不变集是正的。 首席研究员将研究在某些参数空间中接近费根鲍姆极限的系统。 倍周期分岔的这种限制引起了各种物理和生物科学领域的研究人员的强烈兴趣。 一旦超过这个界限，混乱就会开始。