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Lyapunov Exponents for the Random Product of Two Shears
Authors:Sturman  Rob  Thiffeault  Jean-Luc
Affiliation:1.Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
;2.Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr, Madison, WI, 53706, USA
;
Abstract:

We give lower and upper bounds on both the Lyapunov exponent and generalised Lyapunov exponents for the random product of positive and negative shear matrices. These types of random products arise in applications such as fluid stirring devices. The bounds, obtained by considering invariant cones in tangent space, give excellent accuracy compared to standard and general bounds, and are increasingly accurate with increasing shear. Bounds on generalised exponents are useful for testing numerical methods, since these exponents are difficult to compute in practice.

Keywords:
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