{"id":1762,"date":"2019-12-02T16:10:13","date_gmt":"2019-12-02T14:10:13","guid":{"rendered":"https:\/\/sofs.org.ua\/?page_id=1762"},"modified":"2021-01-27T17:54:17","modified_gmt":"2021-01-27T15:54:17","slug":"1-8","status":"publish","type":"page","link":"https:\/\/sofs.org.ua\/en\/sample-page\/arhiv\/2018-2\/2019-4-106\/1-8\/","title":{"rendered":"1.8"},"content":{"rendered":"

EVOLUTION OF THE ERGODIC THEORY\u00a0<\/strong><\/p>\n

1 <\/sup>\u0422.<\/strong>V. <\/strong>KILOCHYTSKA
\n<\/strong>https:\/\/orcid.org\/0000-0003-4471-0904
\n<\/a>1<\/sup> T.H. Shevchenko National University \u201cChernihiv Collegium\u201d<\/strong><\/p>\n

Nauka naukozn. 2019, 4(106): 102-115
\nhttps:\/\/doi.org\/10.15407\/sofs2019.04.102<\/a><\/p>\n

Section<\/strong>: Science and technology history
\nLanguage<\/strong>: Ukrainian
\nAbstract<\/strong>: The article provides a historical reconstruction of the origin, formation and development of the ergodic theory in the global context.<\/p>\n

In 30s of the past century the applied tasks assisted formulation of the theory of nonlinear fluctuations, forming of bases of ergodic theory. G.\u00a0Birkhoff laid the beginning to the concept of the dynamic system. In 1930s ideas of H.\u00a0Poincar\u00e9 laid the beginning of the ergodic theory (G.\u00a0Birkhoff, John von Neumann, M.\u00a0Krylov, M.\u00a0Bogolubov).<\/p>\n

The article describes the historical sequence of becoming and development of the ergodic theory in Ukraine (world context). In 1950\u20131970, the theory of the dynamical systems was rapidly developing. The ergodic theory develops as cleanly mathematical theory within the framework of the general theory of the dynamical systems and studies of transformation with an invariant measure.<\/p>\n

The article shows ways of developing a set of concepts and ideas that resulted in creating of the ergodic theory (for example, in 1934 M.\u00a0Bogolubov and M.\u00a0Krylov introduced the concept of integral manifold, put beginning to asymptotic theory of nonlinear mechanics, in 1958\u20131959 \u0410.\u00a0\u041a\u043elmogorov introduced two fundamental concepts\u00a0\u2013 \u041a-system and dynamical entropy, in 1959 Yakov Sinai developed a concept of entropy, in 1965 three American mathematicians put beginning to the concept of topological entropy).<\/p>\n

In the article, opening is considered from the ergodic theory of the dynamic systems of \u0410.\u00a0\u041a\u043elmogorov and his followers. Dynamical entropy is well-known as entropy of \u041a\u043elmogorov\u00a0\u2013 Sinai entropy\u00a0(1959).<\/p>\n

Numerous works are analyzed, published since 1979, in which the problem of classification of measures was examined on Cantor sets. Probability measures were studied in these works only, majority of results touched the case of Bernoulli measures.<\/p>\n

\u0422he article shows the contribution of Ukrainian scientists in formation of ergodic theory. Works of ergodic theory of M.\u00a0Bogolubov and M.\u00a0Krylov are analyzed. A review of works of the Kharkiv school, devoted to the ergodic theory, is made. Expansion of research directions, research of the dynamical systems operating in spaces of various nature are a modern tendency.<\/p>\n

Keywords<\/strong>:<\/strong> ergodic theorem<\/strong>, ergodic process, <\/strong>ergodic<\/strong> theory<\/strong>,<\/strong> dynamical<\/strong> system<\/strong>, <\/strong>invariant measure<\/strong>.<\/strong><\/p>\n

REFERENCES<\/strong><\/p>\n

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    EVOLUTION OF THE ERGODIC THEORY\u00a0 1 \u0422.V. KILOCHYTSKA https:\/\/orcid.org\/0000-0003-4471-0904 1 T.H. Shevchenko National University \u201cChernihiv Collegium\u201d Nauka naukozn. 2019, 4(106): 102-115 https:\/\/doi.org\/10.15407\/sofs2019.04.102 Section: Science and technology history Language: Ukrainian Abstract: The article provides a historical reconstruction of the origin, formation and development of the ergodic theory in the global context. In 30s of the past […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1693,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"translation":{"provider":"WPGlobus","version":"2.12.2","language":"en","enabled_languages":["uk","en","ru"],"languages":{"uk":{"title":true,"content":true,"excerpt":false},"en":{"title":true,"content":true,"excerpt":false},"ru":{"title":true,"content":true,"excerpt":false}}},"yoast_head":"\n1.8 - Science and Science of Science<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sofs.org.ua\/sample-page\/arhiv\/2018-2\/2019-4-106\/1-8\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"1.8 - Science and Science of Science\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sofs.org.ua\/sample-page\/arhiv\/2018-2\/2019-4-106\/1-8\/\" \/>\n<meta property=\"og:site_name\" content=\"Science and Science of Science\" \/>\n<meta property=\"article:modified_time\" content=\"2021-01-27T15:54:17+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"10 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sofs.org.ua\/sample-page\/arhiv\/2018-2\/2019-4-106\/1-8\/\",\"url\":\"https:\/\/sofs.org.ua\/sample-page\/arhiv\/2018-2\/2019-4-106\/1-8\/\",\"name\":\"1.8 - 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