Abstract: In this talk we will discuss the escape rate of an open dynamical system: the exponential rate at which the mass of the system leaks through a hole. We will go over some recent progress in this problem and their connection with other open questions such as the dimension-drop conjecture. We will prove that for a sequence of nested holes surrounding a compact measure zero set, the localized escape rate converges to the extremal index of the set, provided that the dynamical system is mixing at a sufficient speed. Examples include a dichotomy between periodic and non-periodic points, Cantor sets on the interval, and submanifolds of Anosov diffeomorphisms on surfaces. This is a joint work with Nicolai Haydn and Connor Davis.
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https://msu.zoom.us/j/94702757391
Meeting ID: 947 0275 7391
Passcode: 654321
