Observable Lyapunov irregular sets for planar piecewise expanding maps

Yushi Nakano, Teruhiko Soma, Kodai Yamamoto

For any integer $r$ with $1\le r<\infty$, we present a one-parameter family $F_{\sigma }$ $(0<\sigma <1)$ of 2-dimensional piecewise ${\mathcal{C}}^r$ expanding maps such that each $F_{\sigma }$ has an ob…