Period doubling, entropy, and renormalization
动力系统
2009-09-25 v1
摘要
We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point, i.e., the combinatorial description of the boundary of chaos coincides with the topological description. We also show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable.
引用
@article{arxiv.math/9511221,
title = {Period doubling, entropy, and renormalization},
author = {Jun Hu and Charles Tresser},
journal= {arXiv preprint arXiv:math/9511221},
year = {2009}
}