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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Barreira, L. and Pesin, Ya., Lyapunov exponents and smooth ergodic theory, University Lecture Series, vol. 23 (American Mathematical Society, Providence, RI, 2002). Google Scholar

[2] 2. Barreira, L. and Valls, C., Characterization of stable manifolds for nonuniform exponential dichotomies, Discrete Contin. Dyn. Syst. 21 (2008), 1025–1046. Google Scholar | DOI

[3] 3. Barreira, L. and Valls, C., Nonuniform exponential contractions and Lyapunov sequences, J. Differ. Equ. 246 (2009), 4743–4771. Google Scholar | DOI

[4] 4. Coppel, W., Dichotomies in stability theory, Lecture Notes in Mathematics, vol. 629 (Springer-Verlag, Berlin-New York, 1978). Google Scholar | DOI

[5] 5. Hale, J., Asymptotic behavior of dissipative systems, Mathematical Surveys and Monographs, vol. 25 (American Mathematical Society, Providence, RI, 1988). Google Scholar

[6] 6. Henry, D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840 (Springer-Verlag, Berlin-New York, 1981). Google Scholar | DOI

[7] 7. Mañé, R., Lyapounov exponents and stable manifolds for compact transformations, in Geometric dynamics (Rio de Janeiro, 1981) (Palis J., Editor), Lecture Notes in Mathematics, vol. 1007 (Springer, Berlin, 1983), 522–577. Google Scholar | DOI

[8] 8. Pesin, Ya., Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR-Izv. 10 (1976), 1261–1305. Google Scholar | DOI

[9] 9. Ruelle, D., Characteristic exponents and invariant manifolds in Hilbert space, Ann. Math. 115 (2) (1982), 243–290. Google Scholar | DOI

[10] 10. Sell, G. and You, Y., Dynamics of evolutionary equations, Applied Mathematical Sciences, vol. 143 (Springer-Verlag, New York, 2002). Google Scholar

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