A numerical study of infinitely renormalizable area-preserving maps
2012 (English)In: Dynamical systems, ISSN 1468-9367, E-ISSN 1468-9375, Vol. 27, no 3, 283-301 p.Article in journal (Refereed) Published
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.
37E20, 37C15, 37A20, 37M99, renormalization, area-preserving maps, rigidity, co-cycles
Mathematical Analysis Computational Mathematics
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-179272DOI: 10.1080/14689367.2012.673559ISI: 000307441700001OAI: oai:DiVA.org:uu-179272DiVA: diva2:543987
FunderSwedish Research Council, 2010-598