Geodesic
Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators
Studia Mathematica, Tome 116 (1995) no. 3, pp. 225-238

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We discuss the problem of characterizing the possible asymptotic behaviour of the iterates of a sufficiently smooth nonlinear operator acting in a Banach space in small neighbourhoods of a fixed point. It turns out that under natural conditions, for the most part of initial approximations these iterates tend to "lie down" along a finite-dimensional subspace generated by the leading (peripherical) eigensubspaces of the Fréchet derivative at the fixed point and moreover the asymptotic behaviour of "projections" of the iterates on this subspace is determined by the arithmetic properties of the leading eigenvalues.
DOI : 10.4064/sm-116-3-225-238

Petr P. Zabreĭko 1

1 
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Petr P. Zabreĭko. Geometric characteristics for convergence and asymptotics of successive approximations of equations with smooth operators. Studia Mathematica, Tome 116 (1995) no. 3, pp. 225-238. doi: 10.4064/sm-116-3-225-238

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