Geodesic
A $C^1$ Anosov diffeomorphism with a horseshoe that attracts almost any point
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 83-86

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We present an example of a $C^1$ Anosov diffeomorphism with a physical measure such that its basin has full Lebesgue measure and its support is a horseshoe of zero measure.
Keywords: Anosov diffeomorphism, $C^1$-topology, physical measure, thick horseshoe. 
@article{FAA_2017_51_2_a7,
     author = {C. Bonatti and S. S. Minkov and A. V. Okunev and I. S. Shilin},
     title = {A $C^1$ {Anosov} diffeomorphism with a horseshoe that attracts almost any point},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {83--86},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a7/}
}
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C. Bonatti; S. S. Minkov; A. V. Okunev; I. S. Shilin. A $C^1$ Anosov diffeomorphism with a horseshoe that attracts almost any point. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 83-86. http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a7/