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 now work at UCD. Come visit!
Past member of the Mathematical Physics group at the University of Geneva.
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.
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.
- Diabolical Entropy (joint with Nicolae Mihalache).
- Free energy jumps up (joint with Mike Todd)
- Quasistatic dynamical systems (joint with Mikko Stenlund)
To appear, ETDS.
- Line, spiral, dense
To appear, L'Enseignement Mathematique.
- 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.