On the Hyperbolicity of Lorenz Renormalization
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
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.
Cantor Sets, Maps, Universality, Attractor, Points, Onset
Physical Sciences Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-140371DOI: 10.1007/s00220-013-1858-zISI: 000329224200007ScopusID: 2-s2.0-84891659463OAI: oai:DiVA.org:kth-140371DiVA: diva2:690427
QC 201401232014-01-232014-01-232014-01-23Bibliographically approved