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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