# Upper Hausdorff dimension estimates for invariant sets of evolutionary systems on Hilbert manifolds

## Main Article Content

## Abstract

We prove a generalization of the Douady-Oesterl\'{e} theorem on the upper bound of the Hausdorff dimension of an invariant set of a smooth map on an infinite dimensional manifold. It is assumed that the linearization of this map is a noncompact linear operator. A similar estimate is given forthe Hausdorff dimension of an invariant set of a dynamical system generated by a differential equation on a Hilbert manifold.

## Article Details

How to Cite

Kruck, A., & Reitman, V.
(2017).
Upper Hausdorff dimension estimates for invariant sets of evolutionary systems on Hilbert manifolds.

*Proceedings Of Equadiff 2017 Conference,*, 247-254. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/equadiff/article/view/811/570
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Articles