Basin of attraction of cycles of discretizations of dynamical systems with SRB invariant measures

被引:11
作者
Diamond, P
Klemm, A
Kloeden, P
Pokrovskii, A
机构
[1] DEAKIN UNIV,SCH COMPUTAT & MATH,GEELONG,VIC 3217,AUSTRALIA
[2] RUSSIAN ACAD SCI,INST INFORMAT TRANSMISS PROBLEMS,MOSCOW,RUSSIA
关键词
chaos; computation; collapse; computer arithmetic; computer artifact;
D O I
10.1007/BF02179655
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Computer simulations of dynamical systems are discretizations, where the finite space of machine arithmetic replaces continuum state spaces. So any trajectory of a discretized dynamical system is eventually periodic. Consequently, the dynamics of such computations are essentially determined by the cycles of the discretized map. This paper examines the statistical properties of the event that two trajectories generate the same cycle. Under the assumption that the original system has a Sinai-Ruelle-Bowen invariant measure, the statistics of the computed mapping are shown to be very close to those generated by a class of random graphs. Theoretical properties of this model successfully predict the outcome of computational experiments with the implemented dynamical systems.
引用
收藏
页码:713 / 733
页数:21
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