Accurate bounds on Lyapunov exponents for expanding maps of the interval

Abstract

In this short note we describe a simple but remarkably effective method for rigorously estimating Lyapunov exponents for expanding maps of the interval. We illustrate the applicability of this method with some standard examples. * The first author is partly supported by ERC-Advanced Grant 833802-Resonances and EPSRC grant EP/T001674/1 the second author is partly supported by EPSRC grant EP/T001674/1.1 This is equivalent to the map being locally eventually onto, i.e. to saying that there exists N ≥ 1 such that for each 1 ≤ j ≤ n we have f N ((x j , x j+1 )) = I.