## Tokyo Journal of Mathematics

- Tokyo J. Math.
- Volume 40, Number 1 (2017), 165-184.

### Historic Behaviour for Random Expanding Maps on the Circle

#### Abstract

F. Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small random perturbations. The proof is given by establishing a random Markov partition, which follows from a random version of Shub's Theorem on topological conjugacy with the folding maps.

#### Article information

**Source**

Tokyo J. Math., Volume 40, Number 1 (2017), 165-184.

**Dates**

First available in Project Euclid: 8 August 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.tjm/1502179221

**Digital Object Identifier**

doi:10.3836/tjm/1502179221

**Mathematical Reviews number (MathSciNet)**

MR3689984

**Zentralblatt MATH identifier**

1375.37071

**Subjects**

Primary: 37C40: Smooth ergodic theory, invariant measures [See also 37Dxx]

Secondary: 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

#### Citation

NAKANO, Yushi. Historic Behaviour for Random Expanding Maps on the Circle. Tokyo J. Math. 40 (2017), no. 1, 165--184. doi:10.3836/tjm/1502179221. https://projecteuclid.org/euclid.tjm/1502179221