EVENT DETAILS AND ABSTRACT

Title: Fractal dimension of the set of divergent trajectories
Speaker: Yitwah Cheung
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:

Consider a flow on a noncompact metric space $\Omega$ and let $D^+\subset\Omega$ be the set of points whose forward trajectory leaves every compact set. It will be shown that for certain special cases of homogeneous flows the fractal dimension of $D^+$ is equal to $\dim\Omega-1/2$. These empirical observations are in stark contrast to a result of Kleinboch-Margulis '96 which asserts that the set of bounded orbits has have full (Hausdorff) dimension