Open Access
2014 Random interval homeomorphisms
Lluís Alsedà, Michał Misiurewicz
Publ. Mat. 58(S1): 15-36 (2014).


We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where there are two piecewise linear homeomorphisms, one moving points to the right and the other one to the left.


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Lluís Alsedà. Michał Misiurewicz. "Random interval homeomorphisms." Publ. Mat. 58 (S1) 15 - 36, 2014.


Published: 2014
First available in Project Euclid: 19 May 2014

zbMATH: 1326.37016
MathSciNet: MR3211824

Primary: 37C55 , 37C70

Keywords: attractor , random system , Skew product

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. S1 • 2014
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