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On the Hyperbolicity of Lorenz Renormalization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 325, no 1, 185-257 p.Article in journal (Refereed) Published
Abstract [en]

We consider infinitely renormalizable Lorenz maps with real critical exponent alpha > 1 of certain monotone combinatorial types. We prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated two-dimensional strong unstable manifold. For monotone families of Lorenz maps we prove that each infinitely renormalizable combinatorial type has a unique representative within the family. We also prove that each infinitely renormalizable map has no wandering intervals, is ergodic, and has a uniquely ergodic minimal Cantor attractor of measure zero.

Place, publisher, year, edition, pages
2014. Vol. 325, no 1, 185-257 p.
Keyword [en]
Cantor Sets, Maps, Universality, Attractor, Points, Onset
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-140371DOI: 10.1007/s00220-013-1858-zISI: 000329224200007Scopus ID: 2-s2.0-84891659463OAI: oai:DiVA.org:kth-140371DiVA: diva2:690427
Note

QC 20140123

Available from: 2014-01-23 Created: 2014-01-23 Last updated: 2017-12-06Bibliographically approved

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