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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, UE be an open set and f:UE be a C 1 -map. It is shown that if ΛE is a compact set such that f(Λ)Λ and for every xΛ the derivative D x f can be decomposed as a sum of a compact map and a contraction, then the limit capacity (and moreover the Hausdorff dimension) of Λ is finite.

Reviewer: I.U.Bronshtejn

MSC:
37C70Attractors and repellers, topological structure
34K30Functional-differential equations in abstract spaces