scholarly journals Ulam's method for some non-uniformly expanding maps

2010 ◽  
Vol 26 (3) ◽  
pp. 1007-1018 ◽  
Author(s):  
Rua Murray ◽  
Keyword(s):  
Expanding Maps ◽  
Ulam’S Method ◽  
Ulam's Method

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

2018 ◽  
Vol 39 (10) ◽  
pp. 2769-2792
Author(s):  
GARY FROYLAND ◽  
CECILIA GONZÁLEZ-TOKMAN ◽  
RUA MURRAY
Keyword(s):  
Invariant Measures ◽  
Single Step ◽  
Absolutely Continuous ◽  
Random Maps ◽  
Driving Mechanisms ◽  
The Family ◽  
Ulam’S Method ◽  
Ulam's Method ◽  
Invariant Densities ◽  
Absolutely Continuous Invariant

The paper by Froyland, González-Tokman and Quas [Stability and approximation of random invariant densities for Lasota–Yorke map cocycles.Nonlinearity27(4) (2014), 647] established fibrewise stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota–Yorke maps under a variety of perturbations, including ‘Ulam’s method’, a popular numerical method for approximating acims. The expansivity requirements of Froylandet alwere that the cocycle (or powers of the cocycle) should be ‘expanding on average’ before applying a perturbation, such as Ulam’s method. In the present work, we make a significant theoretical and computational weakening of the expansivity hypotheses of Froylandet al, requiring only that the cocycle be eventually expanding on average, and importantly,allowing the perturbation to be applied after each single step of the cocycle. The family of random maps that generate our cocycle need not be close to a fixed map and our results can handle very general driving mechanisms. We provide a detailed numerical example of a random Lasota–Yorke map cocycle with expanding and contracting behaviour and illustrate the extra information carried by our fibred random acims, when compared to annealed acims or ‘physical’ random acims.

Ulam's method for random interval maps

Nonlinearity ◽  
1999 ◽  
Vol 12 (4) ◽  
pp. 1029-1051 ◽  
Author(s):  
Gary Froyland
Keyword(s):  
Random Interval ◽  
Interval Maps ◽  
Ulam’S Method ◽  
Ulam's Method

scholarly journals Ulam's Method for Lasota--Yorke Maps with Holes

2014 ◽  
Vol 13 (2) ◽  
pp. 1010-1032 ◽  
Author(s):  
Christopher Bose ◽  
Gary Froyland ◽  
Cecilia González-Tokman ◽  
Rua Murray
Keyword(s):  
Ulam’S Method ◽  
Ulam's Method

scholarly journals The exact rate of approximation in Ulam's method

2001 ◽  
Vol 7 (1) ◽  
pp. 219-235 ◽  
Author(s):  
Christopher Bose ◽  
◽  
Rua Murray ◽  
Keyword(s):  
Rate Of Approximation ◽  
Ulam’S Method ◽  
Ulam's Method

scholarly journals Stochastic perturbations and Ulam's method for W-shaped maps

2013 ◽  
Vol 33 (5) ◽  
pp. 1937-1944 ◽  
Author(s):  
Paweł Góra ◽  
◽  
Abraham Boyarsky
Keyword(s):  
Stochastic Perturbations ◽  
Ulam’S Method ◽  
Ulam's Method
Sign in / Sign up

Export Citation Format

Share Document