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 amixing invariant probability measure absolutely continuous 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 willdiscuss how to obtain similar results under weaker assumptions, which allows the induced mapnot 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 Markovmaps. 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.