## Topological Methods in Nonlinear Analysis

### Alternating Heegaard diagrams and Williams solenoid attractors in $3$-manifolds

#### Abstract

We find all Heegaard diagrams with the property "alternating" or "weakly alternating"' on a genus two orientable closed surface. Using these diagrams we give infinitely many genus two $3$-manifolds, each admits an automorphism whose non-wandering set consists of two Williams solenoids, one attractor and one repeller. These manifolds contain half of Prism manifolds, Poincaré's homology $3$-sphere and many other Seifert manifolds, all integer Dehn surgeries on the figure eight knot, also many connected sums. The result shows that many kinds of $3$-manifolds admit a kind of "translation" with certain stability.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 2 (2016), 769-798.

Dates
First available in Project Euclid: 13 July 2016

https://projecteuclid.org/euclid.tmna/1468413765

Digital Object Identifier
doi:10.12775/TMNA.2016.033

Mathematical Reviews number (MathSciNet)
MR3559933

Zentralblatt MATH identifier
1375.57029

#### Citation

Wang, Chao; Zhang, Yimu. Alternating Heegaard diagrams and Williams solenoid attractors in $3$-manifolds. Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 769--798. doi:10.12775/TMNA.2016.033. https://projecteuclid.org/euclid.tmna/1468413765

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