Geodesic
Lyapunov Exponents and Invariant Measures on a Projective Bundle
Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 549-561

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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. 
@article{MZM_2017_101_4_a4,
     author = {G. S. Osipenko},
     title = {Lyapunov {Exponents} and {Invariant} {Measures} on a {Projective} {Bundle}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {549--561},
     publisher = {mathdoc},
     volume = {101},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a4/}
}
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G. S. Osipenko. Lyapunov Exponents and Invariant Measures on a Projective Bundle. Matematičeskie zametki, Tome 101 (2017) no. 4, pp. 549-561. http://geodesic.mathdoc.fr/item/MZM_2017_101_4_a4/