# Degenerate cocycle with index-1 and Lyapunov exponents

Nguyen Huu Du, Khanh Duy Trinh, Vu Tien Viet

Research output: Contribution to journalArticle

5 Citations (Scopus)

### Abstract

This paper deals with the solvability of initial-value problem and with Lyapunov exponents for linear implicit random difference equations, i.e. the difference equations where the leading term cannot be solved. An index-1 concept for linear implicit random difference equations is introduced and a formula of solutions is given. Paper is also concerned with a version of the multiplicative theorem of Oseledets type.

Original language English 229-245 17 Stochastics and Dynamics 7 2 https://doi.org/10.1142/S0219493707002013 Published - 2007 Jun 1 Yes

### Fingerprint

Difference equations
Cocycle
Lyapunov Exponent
Difference equation
Initial value problems
Initial Value Problem
Solvability
Multiplicative
Term
Theorem

### Keywords

• Index-1 tractable
• Linear implicit equation Lyapunov exponent
• Random dynamical systems

### ASJC Scopus subject areas

• Modelling and Simulation

### Cite this

Degenerate cocycle with index-1 and Lyapunov exponents. / Du, Nguyen Huu; Trinh, Khanh Duy; Viet, Vu Tien.

In: Stochastics and Dynamics, Vol. 7, No. 2, 01.06.2007, p. 229-245.

Research output: Contribution to journalArticle

Du, Nguyen Huu ; Trinh, Khanh Duy ; Viet, Vu Tien. / Degenerate cocycle with index-1 and Lyapunov exponents. In: Stochastics and Dynamics. 2007 ; Vol. 7, No. 2. pp. 229-245.
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