多峰映射族中非双曲奇异吸引子的丰富性

Abundance of Nonhyperbolic Strange Attractors in Families of Multi-modal Maps

本文考虑多峰映射族中非双曲奇异吸引子的丰富性,证明多维参数空间中存在正测度的参数集合,对应系统具有绝对连续的不变测度.

In this paper we consider the abundance of nonhyperbolic strange attractors for families of multi-modal maps and prove that there exists a positive measure set in the multi-dimensional parameter space such that the corresponding systems admit absolutely continuous invariant measures.