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Mat. Zametki, 2017, Volume 101, Issue 4, Pages 549–561 (Mi mz11102)  

This article is cited in 1 scientific paper (total in 1 paper)

Lyapunov Exponents and Invariant Measures on a Projective Bundle

G. S. Osipenko

Sevastopol Branch of the M.V. Lomonosov Moscow State University

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.


DOI: https://doi.org/10.4213/mzm11102

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English version:
Mathematical Notes, 2017, 101:4, 666–676

Bibliographic databases:

UDC: 517
Received: 25.01.2016
Revised: 15.09.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. S. Osipenko, “The spectrum of the averaging of a function over pseudotrajectories of a dynamical system”, Sb. Math., 209:8 (2018), 1211–1233  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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