On cusps and flat tops

Abstract

We develop non-invertible Pesin theory for a new class of maps called cusp maps. These maps may have unbounded derivative, but nevertheless verify a property analogous to $C^{1+\epsilon }$. We do not require the critical points to verify a non-flatness condition, so the results are applicable to $C^{1+\epsilon }$ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.

32 pages, some revisions from the previous version (thanks again, referee!), but the substance remains the same. This version is from Dec 2012

Cited by in corpus (3)

• Diabolical entropy
• Perturbing Misiurewicz parameters in the exponential family
• Bernoulli Convolutions and 1D Dynamics