Positive Liapunov exponents and absolute continuity for maps of the interval
- 1 March 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 3 (1) , 13-46
- https://doi.org/10.1017/s0143385700001802
Abstract
We give a sufficient condition for a unimodal map of the interval to have an invariant measure absolutely continuous with respect to the Lebesgue measure. Apart from some weak regularity assumptions, the condition requires positivity of the forward and backward Liapunov exponent of the critical point.Keywords
This publication has 8 references indexed in Scilit:
- Absolutely continuous measures for certain maps of an intervalPublications mathématiques de l'IHÉS, 1981
- Absolutely continuous invariant measures for one-parameter families of one-dimensional mapsCommunications in Mathematical Physics, 1981
- On the abundance of aperiodic behaviour for maps on the intervalCommunications in Mathematical Physics, 1980
- Invariant measures for Markov maps of the intervalCommunications in Mathematical Physics, 1979
- Invariant Measures and Equilibrium States for Some Mappings which Expand DistancesTransactions of the American Mathematical Society, 1978
- Invariant measures and equilibrium states for some mappings which expand distancesTransactions of the American Mathematical Society, 1978
- Applications conservant une mesure absolument continue par rapport àdx sur [0, 1]Communications in Mathematical Physics, 1977
- On the Existence of Invariant Measures for Piecewise Monotonic TransformationsPublished by Springer Nature ,1974