Geodesic
On~unstable sets of evolution equations in the neighborhood of critical points of a~stationary curve
Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 39-70.

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Equations of the form $\partial_t u=A(u,\lambda)$ are considered, for example, parabolic and hyperbolic equations. It is proved that the change of the local unstable invariant manifolds of such equations is determined by the form of the stationary curve $(u,\lambda)=(U(\xi),\Lambda(\xi))$, $A(u,\lambda)=0$. Bibliography: 9 titles. 
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A. V. Babin; M. I. Vishik. On~unstable sets of evolution equations in the neighborhood of critical points of a~stationary curve. Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 39-70. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a2/

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[5] Babin A. V., Vishik M. I., “O statsionarnykh krivykh i neustoichivykh invariantnykh mnogoobraziyakh v okrestnosti kriticheskikh tochek evolyutsionnykh uravnenii, zavisyaschikh ot parametra”, Dokl. AN SSSR, 280:1 (1985), 19–23 | MR | Zbl

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[9] Hirsch M., Pugh C., Shub M., Invariant Manifolds, Lecture Notes in Math., 583, Springer, 1977 | MR | Zbl