Geodesic
Ergodic Properties of a Transformation of a Self-Similar Space with a Hausdorff Measure
Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 163-173 Cet article a éte moissonné depuis la source Math-Net.Ru

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On a space equipped with a Hausdorff measure and possessing the self-similarity property, we prove ergodicity and study the continuity of the transformation generated by the shift transformation on a sequence space.
Keywords: Hausdorff measure, self-similarity, ergodicity
Mots-clés : fractal, chaos. 
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N. S. Arkashov. Ergodic Properties of a Transformation of a Self-Similar Space with a Hausdorff Measure. Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 163-173. http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a0/

[1] R. M. Kronover, Fraktaly i khaos v dinamicheskikh sistemakh, Postmarket, M., 2000

[2] Z. Nitetski, Vvedenie v differentsialnuyu dinamiku, Mir, M., 1975 | MR | Zbl

[3] G. Edgar, Measure, Topology, and Fractal Geometry, Undergrad. Texts Math., Springer, New York, 2008 | MR | Zbl

[4] P. Khalmosh, Teoriya mery, IL, M., 1953 | MR | Zbl

[5] A. N. Shiryaev, Veroyatnost, Nauka, M., 1980 | MR | Zbl

[6] G. M. Zaslavskii, Gamiltonov khaos i fraktalnaya dinamika, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2010

[7] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl

[8] P. Khalmosh, Lektsii po ergodicheskoi teorii, Izd-vo Udmurtsk. un-ta, Izhevsk, 1999