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INVARIANT MEASURES OF STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS USING FOURIER APPROXIMATIONS

Title:

INVARIANT MEASURES OF STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS USING FOURIER APPROXIMATIONS

ISLAM, MD SHAFIQUL and GÓRA, PAWEŁ (2011) INVARIANT MEASURES OF STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS USING FOURIER APPROXIMATIONS. International Journal of Bifurcation and Chaos, 21 (01). pp. 113-123. ISSN 0218-1274

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Official URL: http://dx.doi.org/10.1142/S0218127411028283

Abstract

We consider dynamical system τ : [0, 1] → [0, 1] and its stochastic perturbations , N ≥ 1. Using Fourier approximation, we construct a finite dimensional approximation PN to a perturbed Perron–Frobenius operator. Let be an invariant density of τ and be a fixed point of PN. We show that converges in L1 to .

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:ISLAM, MD SHAFIQUL and GÓRA, PAWEŁ
Journal or Publication:International Journal of Bifurcation and Chaos
Date:2011
Digital Object Identifier (DOI):10.1142/S0218127411028283
Keywords:Stochastic perturbations of dynamical systems; Fourier approximation; Frobenius–Perron operator; probability density function; absolutely continuous invariant measures
ID Code:976828
Deposited By: DANIELLE DENNIE
Deposited On:29 Jan 2013 14:17
Last Modified:18 Jan 2018 17:43

References:

L. Billings and E. M. Bollt, Chaos Solit. Fract. 12, 365 (2001), DOI: 10.1016/S0960-0779(99)00204-0 .
E. Bollt, SIAM J. Appl. Dyn. Syst. 7, 341 (2008), DOI: 10.1137/070686111 .
A. Boyarsky and P. Góra, Laws of Chaos (Birkhaüser, 1997).
A. Boyarsky and P. Góra, J. Appl. Math. Stochast. Anal. 14, 257 (2001), DOI: 10.1155/S1048953301000211 .
P. Góra, Colloquium Math. XLIX, 73 (1984).
A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics, Applied Mathematical Sciences 97 (Springer-Verlag, NY, 1994).
A. Lasota and J. A. Yorke, Trans. Amer. Math. Soc. 186, 481 (1973), DOI: 10.1090/S0002-9947-1973-0335758-1 .
F. Schweiger, J. Austral. Math. Soc. 34, 55 (1983), DOI: 10.1017/S1446788700019753
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