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A numerical study of infinitely renormalizable area-preserving maps
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. (CAPA)
2012 (English)In: Dynamical systems, ISSN 1468-9367, E-ISSN 1468-9375, Vol. 27, no 3, 283-301 p.Article in journal (Refereed) Published
Abstract [en]

It has been shown in Gaidashev and Johnson [D. Gaidashev and T. Johnson, Dynamics of the universal area-preserving map associated with period doubling: stable sets, J. Mod. Dyn. 3(4) (2009), pp. 555–587.] and Gaidashev et al. [D. Gaidashev, T. Johnson, and M. Martens, Rigidity for infinitely renormalizable area-preserving maps, in preparation.] that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Hölder continuous of exponent α > 0. In this article we investigate numerically the specific value of α. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real.

Place, publisher, year, edition, pages
2012. Vol. 27, no 3, 283-301 p.
Keyword [en]
37E20, 37C15, 37A20, 37M99, renormalization, area-preserving maps, rigidity, co-cycles
National Category
Mathematical Analysis Computational Mathematics
Research subject
URN: urn:nbn:se:uu:diva-179272DOI: 10.1080/14689367.2012.673559ISI: 000307441700001OAI: oai:DiVA.org:uu-179272DiVA: diva2:543987
Swedish Research Council, 2010-598
Available from: 2012-08-13 Created: 2012-08-13 Last updated: 2012-10-01Bibliographically approved

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