Dynamics of complexity of intersections
Dynamics of complexity of intersections
复制标题
交叉口复杂性的动态变化
DOI：
10.1007/bf01236277
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
V. Arnold
中科院分区：
文献类型：
--
作者：
V. Arnold
由动力系统移动的子流形与相空间的给定子流形的相交的拓扑复杂性可以随时间增加。证明了横截交的莫尔斯数和Betti数“一般地”至多呈指数增长，而对于某些特殊的无穷光滑系统，横截交的拓扑复杂性可以大于任何给定的时间函数（对于一个增长的整数时刻序列）.
The topological complexity of the intersection of a submanifold, moved by a dynamical system, with a given submanifold of the phase space, can increase with time. It is proved that the Morse and Betti numbers of the transversal intersections “generically” grow at most exponentially, while for some special infinitely smooth systems the topological complexity of the intersections can become larger than any given function of time (for a growing sequence of integer time moments).