Invariant measures for interval maps without Lyapunov exponents

12 Feb 2021 · Jorge Olivares-Vinales ·

We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and non-flat critical points.