A generic C-1 expanding map has a singular S-R-B measure

Authors
Campbell, JT Quas, AN
Citation
Jt. Campbell et An. Quas, A generic C-1 expanding map has a singular S-R-B measure, COMM MATH P, 221(2), 2001, pp. 335-349
Citations number
20
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
221
Issue
2
Year of publication
2001
Pages
335 - 349
Database
ISI
SICI code
0010-3616(200107)221:2<335:AGCEMH>2.0.ZU;2-J
Abstract
We show that for a generic C-1 expanding map T of the unit circle, there is a unique equilibrium state for - log T' that is an S-R-B measure for T, an d whose statistical basin of attraction has Lebesgue measure 1. We also pre sent some results related to the question of whether a generic C-1 expandin g map preserves a or-finite measure, absolutely continuous with respect to Lebesgue measure.