Geodesic
Number of invariant measures with maximal entropy for translation in the space of sequences
Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 291-302.

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An example is constructed of a topologically transitive dynamic system with positive entropy, having any assigned finite number of ergodic measures with respect to each of which the metric entropy is equal to the topological entropy. 
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     author = {M. S. Shtil'man},
     title = {Number of invariant measures with maximal entropy for translation in the space of sequences},
     journal = {Matemati\v{c}eskie zametki},
     pages = {291--302},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a7/}
}
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M. S. Shtil'man. Number of invariant measures with maximal entropy for translation in the space of sequences. Matematičeskie zametki, Tome 9 (1971) no. 3, pp. 291-302. http://geodesic.mathdoc.fr/item/MZM_1971_9_3_a7/