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Zbl 0544.58014
Mañé, Ricardo
On the dimension of the compact invariant sets of certain non-linear maps.
(English)
[A] Dynamical systems and turbulence, Proc. Symp., Coventry 1980, Lect. Notes Math. 898, 230-242 (1981).

[For the entire collection see Zbl 0465.00017.] \par Let E be a Banach space, $U\subset E$ be an open set and f:$U\to E$ be a $C\sp 1$-map. It is shown that if $\Lambda \subset E$ is a compact set such that $f(\Lambda)\supset \Lambda$ and for every $x\in \Lambda$ the derivative $D\sb xf$ can be decomposed as a sum of a compact map and a contraction, then the limit capacity (and moreover the Hausdorff dimension) of $\Lambda$ is finite.
[I.U.Bronshtejn]
MSC 2000:
*37C70 Attractors and repellers, topological structure
34K30 Functional-differential equations in abstract spaces

Keywords: Banach space; limit capacity; Hausdorff dimension

Citations: Zbl 0465.00017

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