Tokyo Journal of Mathematics

Historic Behaviour for Random Expanding Maps on the Circle

Yushi NAKANO

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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


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