Abstract:
The paper is concerned with the discrete dynamical system generated by a homeomorphism f on a compact manifold M and with a continuous function φ. The averaging of φ over a periodic ε-trajectory is the arithmetic mean of the values of φ on the period. The limit set as ε→0 of the averagings over periodic ε-trajectories is called the spectrum of the averaging. The spectrum is shown to consist of closed intervals, where each interval is generated by a component of the chain recurrent set and can be obtained by averaging the function φ over all invariant measures concentrated on this component.
Bibliography: 18 titles.
Citation:
G. S. Osipenko, “The spectrum of the averaging of a function over pseudotrajectories of a dynamical system”, Sb. Math., 209:8 (2018), 1211–1233
\Bibitem{Osi18}
\by G.~S.~Osipenko
\paper The spectrum of the averaging of a~function over pseudotrajectories of a~dynamical system
\jour Sb. Math.
\yr 2018
\vol 209
\issue 8
\pages 1211--1233
\mathnet{http://mi.mathnet.ru/eng/sm8970}
\crossref{https://doi.org/10.1070/SM8970}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3833537}
\zmath{https://zbmath.org/?q=an:1407.37036}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018SbMat.209.1211O}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000448025000005}
\elib{https://elibrary.ru/item.asp?id=35276522}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85055803702}
Linking options:
https://www.mathnet.ru/eng/sm8970
https://doi.org/10.1070/SM8970
https://www.mathnet.ru/eng/sm/v209/i8/p114
This publication is cited in the following 2 articles:
G. S. Osipenko, “Encodings of trajectories and invariant measures”, Sb. Math., 211:7 (2020), 1041–1064
G. S. Osipenko, “Mean Convergence of Periodic Pseudotrajectories and Invariant Measures of Dynamical Systems”, Math. Notes, 108:6 (2020), 854–866
Citation in format AMSBIB
Contact us: