Persistence of Semi-Trajectories |
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Authors: | Jorge Lewowicz |
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Institution: | (1) IMERL. Facultad de Ingenieria, Julio Herrera y Reissig 565, C.P., 11.300 Montevideo, Uruguay |
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Abstract: | We consider diffeomorphisms f of a smooth compact riemannian mainfold M and its suspension flow
. Assuming some regularity of the stable (unstable) sets at the points
we prove the persistence in the future of {f
n
(x), n ≥ 0} or
, i.e., that C
0 small perturbations g of f have a semi-trajectory that closely shadows {f
n
(x), n ≥ 0} and that the suspension of g has also a semi-trajectory that closely shadows
. In case x belongs to a minimal set of f we show that the assumptions concerning the regularity of stable and unstable sets could be reduced to a neighbourhood of x. |
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Keywords: | Expansive diffeomorphisms stable set unstable set suspension Lyapunov function persistence shadowing semi-conjugacy minimal set |
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