Geodesic
Limiting curves for polynomial adic systems
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 177-200

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We prove the existence of limiting curves (describing deviations in the ergodic theorem) for cylinder functions for polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by E. Janvresse, T. de la Rue, and Y. Velenik. 
@article{ZNSL_2016_448_a12,
     author = {A. R. Minabutdinov},
     title = {Limiting curves for polynomial adic systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {177--200},
     publisher = {mathdoc},
     volume = {448},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a12/}
}
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A. R. Minabutdinov. Limiting curves for polynomial adic systems. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 177-200. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a12/