21 citations · 98 across the 15 of their papers we have counts for
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math.DS2008★ 6 cited
Measures with positive Lyapunov exponent and conformal measures in rational dynamics
Neil Dobbs
Ergodic properties of rational maps are studied, generalising the work of F.\ Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal m…
math.DS2008★ 10 cited
On cusps and flat tops
Neil Dobbs
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 …
math.DS2008
Non-existence of absolutely continuous invariant probabilities for exponential maps
Neil Dobbs, Bartlomiej Skorulski
We show that for entire maps of the form such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuo…