Geodesic
LOWER BOUNDS ALONG STABLE MANIFOLDS
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 527-537

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It is well known that along any stable manifold the dynamics travels with an exponential rate. Moreover, this rate is close to the slowest exponential rate along the stable direction of the linearization, provided that the nonlinear part is sufficiently small. In this note, we show that whenever there is also a fastest finite exponential rate along the stable direction of the linearization, similarly we can establish a lower bound for the speed of the nonlinear dynamics along the stable manifold. We consider both cases of discrete and continuous time, as well as a nonuniform exponential behaviour. 
BARREIRA, LUIS; VALLS, CLAUDIA. LOWER BOUNDS ALONG STABLE MANIFOLDS. Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 527-537. doi: 10.1017/S001708951700026X
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     author = {BARREIRA, LUIS and VALLS, CLAUDIA},
     title = {LOWER {BOUNDS} {ALONG} {STABLE} {MANIFOLDS}},
     journal = {Glasgow mathematical journal},
     pages = {527--537},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S001708951700026X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951700026X/}
}
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