Foias, C.; Olson, E. Finite fractal dimension and Hölder-Lipschitz parametrization. (English) Zbl 0887.54034 Indiana Univ. Math. J. 45, No. 3, 603-616 (1996). The authors first extend the Hölder-Mañé Theorem [A. Ben-Artzi, A. Eden, C. Foiaş and B. Nicolaenko, J. Math. Anal. Appl. 178, No. 1, 22-29 (1993; Zbl 0815.46016)] from a finite dimensional space to the general Hilbert space setting. Namely, if \(H\) is a real Hilbert space and \(X\subset H\) has fractal dimension less than \(m/2\), then for any orthogonal projection \(\widetilde P\) such that \(|P-\widetilde P|<\delta\) and \(\widetilde P|_{X}\) has Hölder inverse. Moreover, for any metric space \(M\) of finite fractal dimension less than \(m/2\) there exists a Lipschitz function \(g:H\to {\mathbf R}^m\) with Hölder inverse on its image. Reviewer: Guo Boling (Beijing) Cited in 1 ReviewCited in 34 Documents MSC: 54H20 Topological dynamics (MSC2010) Keywords:finite fractal dimension; orthogonal projection; Hölder inverse Citations:Zbl 0815.46016 PDFBibTeX XMLCite \textit{C. Foias} and \textit{E. Olson}, Indiana Univ. Math. J. 45, No. 3, 603--616 (1996; Zbl 0887.54034) Full Text: DOI