Renormalization and alpha-limit set for expanding Lorenz maps
动力系统
2009-06-17 v2 数学物理
math.MP
摘要
We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of periodic orbit of minimal period, the minimal completely invariant closed set is constructed. Topological characterizations of the renormalizations and -limit sets are obtained via consecutive renormalizations. Some properties of periodic renormalizations are collected in Appendix.
引用
@article{arxiv.math/0703777,
title = {Renormalization and alpha-limit set for expanding Lorenz maps},
author = {Yiming Ding},
journal= {arXiv preprint arXiv:math/0703777},
year = {2009}
}
备注
22 pages, 1 figure