Absolutely continuous invariant measure of a map from grazing-impact oscillators

作者：Li Denghui^*; Xie Jianhua

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2015, 379(10-11): 901-906.

DOI：10.1016/j.physleta.2015.01.015

• Grazing-impact oscillators
• Nordmark map
• Induced Markov map
• Absolutely continuous invariant measures

In this paper we investigate a one-dimensional map with unbounded derivative. The map is the limit of the Nordmark map which is the normal form of a discrete time representation of impact oscillators near grazing, i.e. when the dissipation of the systems is large, the Nordmark map can be viewed as a perturbation of the one-dimensional map. We prove that the map has an ergodic absolutely continuous invariant probability measure in a region of parameter space by constructing an induced Markov map.

• 出版日期2015-5-8
• 单位西南交通大学