Speaker: Asad Ullah (SIMIS)
Abstract: In [2, 3], L. S. Young introduced induced Gibbs Markov maps. It was shown that the existence of induced Gibbs Markov maps with integrable return time implies the existence of an exact invariant absolutely continuous probability measure with respect to reference measure, and the rate of decay of correlations is related to the tail of the return time. In this talk, I will discuss how to obtain similar results under weaker assumptions, which allows the induced map not necessarily to be full branch. The main results presented in this talk are detailed in [1]. [1] Ullah, A., Vilarinho, H. Statistical properties of dynamical systems via induced weak Gibbs Markov maps. Nonlinearity 38 (2025), 045024. [2] Young, L.-S. Statistical properties of dynamical systems with some hyperbolicity. Ann. of Math. (2) 147, 3 (1998), 585-650. [3] Young, L.-S. Recurrence times and rates of mixing. Israel J. Math. 110 (1999), 153-188.
Time: 2025-07-22 14:00:00
Location: R1710, SIMIS
Zoom Meeting ID: 844 0594 7424 (Passcode 076895)
Introduction to the Speaker: Asad Ullah is currently a postdoct at SIMIS. He completed his PhD at the Universidade da Beira Interior, Portugal, under the supervision of Professor Helder Vilarinho. Prior to his PhD, he earned a postgraduate diploma in mathematics from the International Centre for Theoretical Physics (ICTP), Italy. His research lies in the field of Ergodic Theory, with a particular interest in the statistical properties of dynamical systems that admit good inducing schemes.
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