On cusps and flat tops

Details On cusps and flat tops On cusps and flat tops

2008-01-24

arxiv.org/abs/0801.3815v2

Mathematics

Dynamical Systems

31 pages, what's new? Many revisions following a referee's comments [Thanks!]. Subsection 1.2.1 forgoes the condition on the d

Scientific paper

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.

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