Rigorous bounds on Lyapunov exponents of linked twist maps

Abstract

Rigorous, elementary upper and lower bounds upon the Lyapunov exponents of a parametrised family of linked twist maps are given, and obtained explicitly for a specific range of parameter values. The method used to obtain the bounds utilises the existence of invariant cones for specific products of the underlying family of shear maps, and the return time partition of the overlap region of the two annuli. Improvements upon the accuracy of this method are then obtained by considering preceding sequences of matrices on the orbits.