Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps-Reference-Cited by-同舟云学术

Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps

Published:1992-03 Issue:1 Volume:12 Page:13-37
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Benedicks Michael,Young Lai-Sang

Abstract

AbstractWe study the quadratic family and show that for a positive measure set of parameters the map has an absolutely continuous invariant measure that is stable under small random perturbations.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

1. On Iterations of 1 - ax 2 on (- 1,1)

2. Topological and metric properties of 1-dimensional endomorphisms;Jakobson;Sov. Math. Dokl.,1978

3. On the abundance of aperiodic behaviour for maps on the interval

4. Positive measure sets of ergodic rational maps

Cited by 64 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stochastic stability for partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers;Stochastics and Dynamics;2023-06

2. Random Gibbs $ u $-state for partially hyperbolic on fibers system;Discrete and Continuous Dynamical Systems;2023

3. Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps;Annales de l'Institut Henri Poincaré C, Analyse non linéaire;2022-02-25

4. On the timescale at which statistical stability breaks down;Annales de l'Institut Henri Poincaré C, Analyse non linéaire;2021-02

5. Entropy formula and continuity of entropy for piecewise expanding maps;Annales de l'Institut Henri Poincaré C, Analyse non linéaire;2021-02