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2021 NCTS Seminar on Dynamical Systems
 
16:00 - 17:00, December 7, 2021 (Tuesday)
Zoom, Online seminar
(線上演講 Zoom)
Badly Approximable and Non-recurrent Sets for Expanding Markov Maps
Na Yuan (South China University of Technology)

Abstract:

In this talk, we consider the asymptotic behaviors of the orbits of an expanding Markov system ([0, 1], f ) and prove that the badly approximable set is of full Hausdorff dimension. Consequently, the Hansdorff dimension of the set of non-recurrent points is also full. The results can be applied to -transformations, Gauss maps and Lüroth maps etc.

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