Neil Dobbs' preprints/publications
and his 2015
PhD thesis: Critical points, cusps and induced expansion in dimension one
Supervisor: Jacek Graczyk.
Defended on 11th December 2006, Orsay.
I work in the School of Mathematics and Statistics at UCD. Come visit!
My research career has been supported by the French government, the Marie Curie network CODY, the Wallenberg Foundation, the Gustafsson Foundation, an IBM Herman Goldstine Fellowship, the Academy of Finland and the ERC.
I organise the UCD Junior Maths Enrichment activities.
Versions of the first n of the following are on my Arxiv page. My googlescholar page may also be of interest. The arxiv/preprint versions are provided for convenience and may differ from the published versions; read at your own risk.
- Free energy and equilibrium states for families of interval maps (joint with Mike Todd and previously known as 'Free energy jumps up').
Memoirs of the AMS 2023; Volume 286, Number 1417.
- Hausdorff Dimension of Julia Sets in the Logistic Family. (joint with Jacek Graczyk and Nicolae Mihalache).
Comm. Math. Phys. 399, pages 673–716 (2023), doi 10.1007/s00220-022-04568-7
Knobbly but nice.
Ergodic Theory Dynam. Systems Link.
- On the timescale at which statistical stability breaks down. (joint with Alexey Korepanov).
Ann. IHP Analyse Non-linéaire.
- Diabolical Entropy. (joint with Nicolae Mihalache).
Comm. Math. Phys. (2019), doi 10.1007/s00220-019-03293-y
- Quasistatic dynamical systems. (joint with Mikko Stenlund)
Ergodic Theory Dynam. Systems 37 (2017), no. 8, 2556–2596.
- Line, spiral, dense.
L'Enseignement Mathematique. Vol 62, Issue 1/2, 2016, pp. 91-107. doi 10.4171/LEM/62-1/2-6
- Pesin theory and equilibrium measures on the interval.
Fund. Math. 231 (2015), no. 1, 1--17.
- Perturbing Misiurewicz parameters in the exponential family.
Comm. Math. Phys. 335 (2015), no. 2, 571--608
- On cusps and flat tops.
Ann. Inst. Fourier 64(2) (2014), 571-605. A version
- Lattice-free sets, multi-branch split disjunctions, and mixed-integer programming(joint with Sanjeeb Dash, Oktay Gunluk, Tomasz Nowicki and Grzegorz Swirszcz).
Math. Program. 145 (2014) no.1-2 Ser. A.
- Outer billiard around a curvilinear triangle with a fixed diameter (joint with Grzegorz Swirszcz and Tomasz Nowicki).
Publ. Mat. 58 (2014), suppl., 179--194.
- Aprproximation algorithms for the joint replenishment problem with deadlines. (Joint with Marcin Bienkowski, Jaroslaw Byrka, Marek Chrobak, Tomasz Nowicki, Maxim Sviridenko, Grzegorz Swirszcz, Neal Young!).
Automata, Languages, and programming. Part I, 135-147, Lect Notes in Comp Sci, 7965, 2013.
- Measures with positive Lyapunov exponent and conformal measures in rational dynamics.
Trans. AMS. 364 (2012), 2803-2824
- Nice sets and invariant densities in complex dynamics.
Math. Proc. Camb. Phil. Soc. 150, No. 1, 157-165 (2011)
- Renormalisation-induced phase transitions for unimodal maps.
Commun. Math. Phys. 286, 377-387 (2009)
- Non-existence of absolutely continuous invariant probabilities for exponential maps (Joint with Bartlomiej Skorulski).
Fundamenta Mathematicae, 198(3):283-287, 2008
- Visible Measures of Maximal Entropy in Dimension One.
Bull. London Math. Soc. 2007 39: 366-376.
- Expanding Cocyles for Interval Maps.
C. R. Math. Acad. Sci. Paris 345 (2007), no. 1, 39--44.
- Hyperbolic Dimension for Interval Maps.
Nonlinearity, Volume 19, Issue 12, 2006.