Nonuniformly expanding 1d maps with logarithmic singularities
Dynamical Systems
2015-05-28 v1
Abstract
For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behavior. This implies the existence of "chaotic" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations.
Cite
@article{arxiv.1106.1707,
title = {Nonuniformly expanding 1d maps with logarithmic singularities},
author = {Hiroki Takahasi and Qiudong Wang},
journal= {arXiv preprint arXiv:1106.1707},
year = {2015}
}
Comments
17 pages, no figure