Geodesic
Schwartzian derivative for multidimensional maps and flows
Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 143-164

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A generalization of Schwartzian derivative to maps and flows in the space $\mathbb R^n$ and in infinite-dimensional spaces is introduced. It is used to study the type of stability loss (soft or hard) for fixed points and periodic trajectories of diffeo-morphisms and flows. In particular, an example of a partial differential equation of reaction-diffusion type is presented for which the conditions of soft loss of stability of a spatially homogeneous solution are verified. 
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     author = {E. A. Sataev},
     title = {Schwartzian derivative for multidimensional maps and flows},
     journal = {Sbornik. Mathematics},
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     volume = {190},
     number = {1},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_1_a4/}
}
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E. A. Sataev. Schwartzian derivative for multidimensional maps and flows. Sbornik. Mathematics, Tome 190 (1999) no. 1, pp. 143-164. http://geodesic.mathdoc.fr/item/SM_1999_190_1_a4/