Palestras e Seminários
04/12/2019
14:00
Sala 4-003
Palestrante: Arthur C. Cunha
Seminário em dinâmica não linear

Abstract: We give a simple proof of a result due to Mañé that a compact subset A of a Banach space that is negatively invariant for a map S is finite-dimensional if D S(x)=C(x)+L(x), where C is compact and L is a contraction (and both are linear). In particular, we show that if S is compact and differentiable then A is finite-dimensional. We also prove some results (following Málek, Ruzicka & Thäter and Zelik that give bounds on the (box-counting) dimension of such sets assuming a 'smoothing property': in its simplest form this requires S to be Lipschitz from X into another Banach space Z that is compactly embedded in X. The resulting bounds depend on the Kolmogorov epsilon-entropy of the embedding of Z into X. We give applications to an abstract semilinear parabolic equation and the two-dimensional Navier--Stokes equations.

 

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