The ergodic theory of positive operators on continuous functions

We give a counterexample showing that $\bar{(I - T *) L_{\infty}} \cap L_{\infty}^{+} = 0$ does not imply the existence of a strictly positive function u in $L_{1}$ with Tu = u, where T is a power bounded positive linear operator on $L_{1}$ of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.

Multiple return times theorems for weakly mixing systems

I. Assani (2000)

Annales de l'I.H.P. Probabilités et statistiques

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Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point

P. Collet, P. Ferrero (1990)

Annales de l'I.H.P. Physique théorique

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