Genus two Smale-Williams solenoids in 3-manifolds
Geometric Topology
2009-08-04 v2 Dynamical Systems
Abstract
Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale-Williams solenoid attractors and repellers, an interesting example is the truncated-cube space. In addition, we prove that if the nonwandering set of the diffeomorphism consists of genus two Smale-Williams solenoids, then the Heegaard genus of the closed manifold is at most two.
Keywords
Cite
@article{arxiv.math/0610474,
title = {Genus two Smale-Williams solenoids in 3-manifolds},
author = {Jiming Ma and Bin Yu},
journal= {arXiv preprint arXiv:math/0610474},
year = {2009}
}
Comments
18 pages, corrected typos