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On the dimension of the compact invariant sets of certain non-linear maps. (English) Zbl 0544.58014
Dynamical systems and turbulence, Proc. Symp., Coventry 1980, Lect. Notes Math. 898, 230-242 (1981).
[For the entire collection see Zbl 0465.00017.]
Let E be a Banach space, \(U\subset E\) be an open set and f:\(U\to E\) be a \(C^ 1\)-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 \(D_ xf\) 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.
Reviewer: I.U.Bronshtejn

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
34K30 Functional-differential equations in abstract spaces