English

Linear operators with infinite entropy

Dynamical Systems 2019-08-02 v1 General Topology

Abstract

We examine the chaotic behavior of certain continuous linear operators on infinite-dimensional Banach spaces, and provide several equivalent characterizations of when these operators have infinite topological entropy. For example, it is shown that infinite topological entropy is equivalent to non-zero topological entropy for translation operators on weighted Lebesgue function spaces. In particular, finite non-zero entropy is impossible for this class of operators, which answers a question raised by Yin and Wei.

Keywords

Cite

@article{arxiv.1908.00291,
  title  = {Linear operators with infinite entropy},
  author = {Will Brian and James P. Kelly},
  journal= {arXiv preprint arXiv:1908.00291},
  year   = {2019}
}