Parameter Spaces of Locally Constant Cocycles
Publisher
DOI
10.1093/imrn/rnab116
Journal
International Mathematics Research Notices
ISSN
1073-7928
Metadata
Show full item recordAbstract
This article concerns the locus of locally constant SL(2,ℝ)
-valued cocycles that have a dominated splitting, called the hyperbolic locus. By developing the theory of Möbius semigroups we show that cocycles on the boundary of the hyperbolic locus, apart from a few exceptions, exhibit some form of hyperbolic behaviour. This behaviour is used to answer a question posed by Avila, Bochi and Yoccoz. Our approach introduces a new locus of cocycles, closely related to the hyperbolic locus, and motivates a line of investigation on the subject.
Authors
Christodoulou, ACollections
- Mathematics [1444]