I hope you enjoy your tour today. Please feel free to roam around and dwell on some of the works in our current exhibit.
Templates act as a model for complicated hyperbolic regions of three-dimensional flows.
The entire geometry of the fibration is contained in this template, which lives in the complement of the figure eight knot. Phil Holmes and Bob Williams used this simplification to prove some striking results about bifurcations in the Henon maps. A gluing bifurcation is also a codimension-two bifurcation of flows which occurs when there are a simultnaeous pair of homoclinic curves. Here are the three relevant bifurcation diagrams. They are all three-dimensional.