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Discrete and Continuous Dynamical Systems - Series S (DCDS-S)
 

On integral separation of bounded linear random differential equations

Pages: 995 - 1007, Volume 9, Issue 4, August 2016      doi:10.3934/dcdss.2016038

 
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Nguyen Dinh Cong - Institute of Mathematics, Vietnamese Academy of Science and Technology, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam (email)
Doan Thai Son - Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Ha Noi, Viet Nam, Vietnam (email)

Abstract: Our aim in this paper is to investigate the openness and denseness for the set of integrally separated systems in the space of bounded linear random differential equations equipped with the $L^{\infty}$-metric. We show that in the general case, the set of integrally separated systems is open and dense. An exception is the case when the base space is isomorphic to the ergodic rotation flow of the unit circle, in which the set of integrally separated systems is open but not dense.

Keywords:  Random differential equations, Lyapunov exponents, integral separation, multiplicative ergodic theorem, genericity.
Mathematics Subject Classification:  Primary: 37A20, 37A10, 37Hxx; Secondary: 34D08.

Received: August 2015;      Revised: January 2016;      Available Online: August 2016.

 References