4:00 pm Wednesday, March 1, 2017
Groups & Dynamics : Non-uniform mixing properties and intrinsic ergodicity for subshifts by Ronnie Pavlov (University of Denver) in RLM 11.176
In topological dynamics, there are a wide range of mixing properties, all of which amount to the ability, given two open sets, to find a point which lies in the first and then, after some number of iterates, lies in the second. In the setting of symbolic dynamics, this can be interpreted as the ability, given two (say n-letter) words in the language of a subshift, to place some gap in between which can be filled to make a new word in the language. When the gap can be chosen with length independent of the words to be combined, we have the celebrated specification property of Bowen which, among other properties, implies intrinsic ergodicity, i.e. uniqueness of the measure of maximal entropy. When the required gap has length f(n) dependent on the length n of the words to be combined, it is natural to wonder whether slow growth of f(n) yields positive properties as well. I will summarize some recent results in this area, mainly focusing on intrinsic ergodicity. The main result I plan to describe is that for a mixing property called non-uniform specification, liminf f(n)/log n = 0 implies intrinsic ergodicity, and liminf f(n)/log n 0 allows for multiple measures of maximal entropy.
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