Universal asymptotics in hyperbolicity breakdown
2008 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 21, no 3, 557-586 p.Article in journal (Refereed) Published
We study a scenario for the disappearance of hyperbolicity of invariant tori in a class of quasi-periodic systems. In this scenario, the system loses hyperbolicity because two invariant directions come close to each other, losing their regularity. In a recent paper, based on numerical results, Haro and de la Llave (2006 Chaos 16 013120) discovered a quantitative universality in this scenario, namely, that the minimal angle between the two invariant directions has a power law dependence on the parameters and the exponents of the power law are universal. We present an analytic proof of this result.
Place, publisher, year, edition, pages
2008. Vol. 21, no 3, 557-586 p.
IdentifiersURN: urn:nbn:se:kth:diva-17401DOI: 10.1088/0951-7715/21/3/010ISI: 000254305500012OAI: oai:DiVA.org:kth-17401DiVA: diva2:335445
QC 201005252010-08-052010-08-052012-04-14Bibliographically approved