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Matematicheskie Zametki, 2017, Volume 101, Issue 4, Pages 549–561
DOI: https://doi.org/10.4213/mzm11102 (Mi mzm11102) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Lyapunov Exponents and Invariant Measures on a Projective Bundle

G. S. Osipenko

Sevastopol Branch of the M.V. Lomonosov Moscow State University
Full-text PDF (478 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11102
Abstract: A discrete dynamical system generated by a diffeomorphism $f$ on a compact manifold is considered. The Morse spectrum is the limit set of Lyapunov exponents of periodic pseudotrajectories. It is proved that the Morse spectrum coincides with the set of averagings of the function $\varphi(x,e)=\ln|Df(x)e|$ over the invariant measures of the mapping induced by the differential $Df$ on the projective bundle.
Keywords: Morse spectrum, chain-recurrent set, projective bundle, invariant measure, symbolic image, flow on a graph, averaging with respect to a measure.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00452
This work was supported in part by the Russian Foundation for Basic Research under grant 16-01-00452.
Received: 25.01.2016
Revised: 15.09.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 4, Pages 666–676
DOI: https://doi.org/10.1134/S0001434617030245
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: G. S. Osipenko, “Lyapunov Exponents and Invariant Measures on a Projective Bundle”, Mat. Zametki, 101:4 (2017), 549–561; Math. Notes, 101:4 (2017), 666–676
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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