21 citations · 98 across the 15 of their papers we have counts for
16 papers
Precise asymptotics at the tip of the Mandelbrot set
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
For the quadratic family , the only parameters in the Mandelbrot set for which the Julia set has Hausdorff dimension are and . Nea…
Hausdorff dimension of Julia sets in the logistic family
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depe…
Knobbly but nice
Neil Dobbs
Our main result states that, under an exponential map whose Julia set is the whole complex plane, on each piecewise smooth Jordan curve there is a point whose orbit is dense. This…
On the timescale at which statistical stability breaks down
Neil Dobbs, Alexey Korepanov
In dynamical systems, understanding statistical properties shared by most orbits and how these properties depend on the system are basic and important questions. Statistical proper…
Diabolical entropy
Neil Dobbs, Nicolae Mihalache
Milnor and Thurston's famous paper proved monotonicity of the topological entropy for the real quadratic family. Guckenheimer showed that it is Hölder continuous. We obtain a preci…
Free energy and equilibrium states for families of interval maps
Neil Dobbs, Mike Todd
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost up…