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Harmonic Averages and New Explicit Constants for Invariant Densities of Piecewise Expanding Maps of the Interval

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Harmonic Averages and New Explicit Constants for Invariant Densities of Piecewise Expanding Maps of the Interval

GÓRA, PAWEŁ, Li, Zhenyang, Boyarsky, Abraham and Proppe, Harald (2012) Harmonic Averages and New Explicit Constants for Invariant Densities of Piecewise Expanding Maps of the Interval. Journal of Statistical Physics, 146 (4). pp. 850-863. ISSN 0022-4715

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Official URL: http://dx.doi.org/10.1007/s10955-012-0425-x

Abstract

The statistical behavior of families of maps is important in studying the stability properties of chaotic maps. For a piecewise expanding map τ whose slope >2 in magnitude, much is known about the stability of the associated invariant density. However, when the map has slope magnitude ≤2 many different behaviors can occur as shown in (Keller in Monatsh. Math. 94(4): 313–333, 1982) for W maps. The main results of this note use a harmonic average of slopes condition to obtain new explicit constants for the upper and lower bounds of the invariant probability density function associated with the map, as well as a bound for the speed of convergence to the density. Since these constants are determined explicitly the results can be extended to families of approximating maps.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:GÓRA, PAWEŁ and Li, Zhenyang and Boyarsky, Abraham and Proppe, Harald
Journal or Publication:Journal of Statistical Physics
Date:2012
Digital Object Identifier (DOI):10.1007/s10955-012-0425-x
Keywords:absolutely continuous invariant measures · piecewise expanding maps of interval · lower bound for invariant density · explicit constants for rate of convergence · harmonic average of slopes
ID Code:976824
Deposited By: DANIELLE DENNIE
Deposited On:29 Jan 2013 13:56
Last Modified:18 Jan 2018 17:43

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