Resumen de Logarithmic Bounds for Ergodic Sums of Certain Flows on the Torus: a Short Proof

Jérôme Carrand

• We give a short proof that the ergodic sums of C1 observables for a C1 flow on T2 admitting a closed transversal curve whose Poincaré map has constant type rotation number have growth deviating at most logarithmically from a linear one. For this, we relate the latter integral to the Birkhoff sum of a well-chosen observable on the circle and use the Denjoy-Koksma inequality. We also give an example of a nonminimal flow satisfying the above assumptions