Continuity properties of transport coefficients in simple maps
Howard PJ, Keller G, Klages R (2008)
Publication Type: Journal article
Publication year: 2008
Journal
Publisher: Institute of Physics: Hybrid Open Access
Book Volume: 21
Pages Range: 1719-1743
DOI: 10.1088/0951-7715/21/8/003
Abstract
We consider families of dynamics that can be described in terms of Perron-Frobenius operators with exponential mixing properties. For piecewise C 2 expanding interval maps we rigorously prove continuity properties of the drift J(λ) and of the diffusion coefficient D(λ) under parameter variation. Our main result is that D(λ) has a modulus of continuity of order O(|δλ|.(log|δλ|) 2), i.e. D(λ) is Lipschitz continuous up to quadratic logarithmic corrections. For a special class of piecewise linear maps we provide more precise estimates at specific parameter values. Our analytical findings are quantified numerically for the latter class of maps by using exact series expansions for the transport coefficients that can be evaluated numerically. We numerically observe strong local variations of all continuity properties. © 2008 IOP Publishing Ltd and London Mathematical Society.
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APA:
Howard, P.J., Keller, G., & Klages, R. (2008). Continuity properties of transport coefficients in simple maps. Nonlinearity, 21, 1719-1743. https://dx.doi.org/10.1088/0951-7715/21/8/003
MLA:
Howard, Phil J., Gerhard Keller, and Rainer Klages. "Continuity properties of transport coefficients in simple maps." Nonlinearity 21 (2008): 1719-1743.
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