CONTROLLING CHAOTIC TRANSPORT THROUGH RECURRENCE

作     者：BOLLT, EM MEISS, JD 

作者机构：Program in Applied Mathematics University of Colorado Boulder CO 80309 USA 

出 版 物：《PHYSICA D》 (物理学D辑：非线性现象)

年 卷 期：1995年第81卷第3期

页      面：280-294页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：NSF Graduate Research Traineeship, (DMS-9208685) National Science Foundation, (DMS-9305847) National Science Foundation North Atlantic Treaty Organization, (CRG 921181) North Atlantic Treaty Organization 

主　　题：Systems Targets Maps maps Segments track time Chaotic systems INITIAL CONDITIONS Relapse 

摘      要：Transport times for a chaotic system are highly sensitive to initial conditions and parameter values. We present a technique to find rough orbits (epsilon chains) that achieve a desired transport rapidly and which can be stabilized with small parameter perturbations. The strategy is to build the epsilon chain from segments of a long orbit - the point is that long orbits have recurrences in neighborhoods where faster orbits must also pass. The recurrences are used as the switching points between segments. The resulting epsilon chain can be refined by gluing orbit segments over the switching points, providing that a local hyperbolicity condition is satisfied. As an example, we show that transport times for the standard map can be reduced by factors of 10(4). The techniques presented here can be easily generalized to higher dimensions and to systems where the dynamics is known only as a time-series.