Geodesic
Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 252-266

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A detailed proof of the absence of mixing is presented for a special flow constructed by an arbitrary rotation of the circle and by a symmetric function with logarithmic singularities (i.e., a function for which the sums of the coefficients of logarithms for “right” and “left” singularities are equal). 
@article{TM_2007_256_a12,
     author = {A. V. Kochergin},
     title = {Nondegenerate {Saddle} {Points} and the {Absence} of {Mixing} in {Flows} on {Surfaces}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {252--266},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_256_a12/}
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A. V. Kochergin. Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 252-266. http://geodesic.mathdoc.fr/item/TM_2007_256_a12/