Examples of expandingC1 maps having no σ-finite invariant measure equivalent to Lebesgue
- 65 Downloads
In this paper we construct aC1 expanding circle map with the property that it has no σ-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.