Examples of expanding C-1 maps having no sigma-finite invariant measure equivalent to Lebesgue

Authors
Bruin, H Hawkins, J
Citation
H. Bruin et J. Hawkins, Examples of expanding C-1 maps having no sigma-finite invariant measure equivalent to Lebesgue, ISR J MATH, 108, 1998, pp. 83-107
Citations number
28
Categorie Soggetti
Mathematics
Journal title
ISRAEL JOURNAL OF MATHEMATICS
ISSN journal
00212172 → ACNP
Volume
108
Year of publication
1998
Pages
83 - 107
Database
ISI
SICI code
0021-2172(1998)108:<83:EOECMH>2.0.ZU;2-7
Abstract
In this paper we construct a C-1 expanding circle map with the property tha t it has no sigma-finite invariant measure equivalent to Lebesgue measure. We extend the construction to interval maps and maps on higher dimensional tori and the Riemann sphere. We also discuss recurrence of Lebesgue measure for the family of tent maps.