|Speaker:||Boris Hasselblatt (Tufts University)|
|Title:||Increasing the complexity of free particle motion by breaking its mechanical nature|
|Date (JST):||Thu, Nov 01, 2018, 15:30 - 17:00|
|Place:||Seminar Room B|
Starting from free particle motion of a negatively curved surface, a Dehn-like surgery on the phase space produces new flows that retain the contact property of a mechanical flow but no longer have a configuration space and are otherwise unusual and interesting. They are no longer topologically equivalent to a flow of an algebraic nature, and they have faster orbit growth. A like surgery on the purely periodic fiber flow makes it parabolic or hyperbolic, a change from no complexity to polynomial or exponential complexity, respectively. Moreover, in all cases the "contact structure" alone forces similar complexity.
Finally, an idea by Vinhage promises a quantification of the complexity increase.