scholarly journals Invariant densities and escape rates: Rigorous and computable approximations in the -norm

2011 ◽  
Vol 74 (13) ◽  
pp. 4481-4495 ◽  
Author(s):  
Wael Bahsoun ◽  
Christopher Bose
Keyword(s):  
Invariant Densities

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.

scholarly journals Existence of invariant densities for semiflows with jumps

2016 ◽  
Vol 435 (1) ◽  
pp. 61-84 ◽  
Author(s):  
Weronika Biedrzycka ◽  
Marta Tyran-Kamińska
Keyword(s):  
Invariant Densities

Mechanisms for Phase Transitions in the Multifractal Analysis of Invariant Densities of Correlated Random Maps

1994 ◽  
Vol 49 (12) ◽  
pp. 1219-1222 ◽  
Author(s):  
Günter Radons
Keyword(s):  
Phase Transitions ◽  
Multifractal Analysis ◽  
Random Maps ◽  
Thermodynamical Formalism ◽  
Invariant Densities

Abstract Multifractal properties of the invariant densities of correlated random maps are analyzed. It is proven that within the thermodynamical formalism phase transitions for finite correlations may be due to transients. For systems with infinite correlations we show analytically that phase transitions can occur as a consequence of localization-delocalization transitions of relevant eigenfunctions.

Sign in / Sign up

Export Citation Format

Share Document