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Researchers at UCD

Neil Dobbs

Lecturer/Assistant Professor

School Of Mathematics & Statistics
Science Centre - South
Belfield
Dublin 4

Tel: +353 1 7162588
Email: neil.dobbs@ucd.ie

Publications

     

Peer Reviewed Journals

Dobbs, Neil (2017) 'Dense yet Elementary'. The Mathematical Intelligencer, :1-4. Available Online [DOI] [Details]
Dobbs, Neil (2016) 'Line, spiral, dense'. Enseign. Math, 62 (1-2):91-107. Available Online [DOI] [Details]
DOBBS, NEIL and STENLUND, MIKKO (2016) 'Quasistatic dynamical systems'. Ergodic Theory and Dynamical Systems, :1â¿¿41. [DOI] [Details]
Dobbs, Neil (2015) 'Perturbing Misiurewicz parameters in the exponential family'. Comm. Math. Phys, 335 (2):571-608. Available Online [DOI] [Details]
Bienkowski, Marcin and Byrka, Jaros\l aw and Chrobak, Marek and Dobbs, Neil and Nowicki, Tomasz and Sviridenko, Maxim and \'Swirszcz, Grzegorz and Young, Neal E. (2015) 'Approximation algorithms for the joint replenishment problem with deadlines'. J. Sched, 18 (6):545-560. Available Online [DOI] [Details]
Dobbs, Neil (2015) 'Pesin theory and equilibrium measures on the interval'. Fund. Math, 231 (1):1-17. Available Online [DOI] [Details]
Dash, Sanjeeb and Dobbs, Neil B. and G\"unl\"uk, Oktay and Nowicki, Tomasz J. and \'Swirszcz, Grzegorz M. (2014) 'Lattice-free sets, multi-branch split disjunctions, and mixed-integer programming'. Math. Program, 145 (1-2, Ser. A):483-508. Available Online [DOI] [Details]
Dobbs, Neil (2014) 'On cusps and flat tops'. Ann. Inst. Fourier (Grenoble), 64 (2):571-605. Available Online [Details]
Dobbs, Neil and Nowicki, Tomasz and \'Swirszcz, Grzegorz (2014) 'Outer billiard around a curvilinear triangle with a fixed diameter'. Publ. Mat, 58 (suppl):179-194. Available Online [Details]
Dobbs, Neil (2012) 'Measures with positive Lyapunov exponent and conformal measures in rational dynamics'. Trans. Amer. Math. Soc, 364 (6):2803-2824. Available Online [DOI] [Details]
Dobbs, Neil (2011) 'Nice sets and invariant densities in complex dynamics'. Math. Proc. Cambridge Philos. Soc, 150 (1):157-165. Available Online [DOI] [Details]
Dobbs, Neil (2009) 'Renormalisation-induced phase transitions for unimodal maps'. Comm. Math. Phys, 286 (1):377-387. Available Online [DOI] [Details]
Dobbs, Neil and Skorulski, Bart\l omiej (2008) 'Non-existence of absolutely continuous invariant probabilities for exponential maps'. Fund. Math, 198 (3):283-287. Available Online [DOI] [Details]
Dobbs, Neil (2007) 'Visible measures of maximal entropy in dimension one'. Bull. Lond. Math. Soc, 39 (3):366-376. Available Online [DOI] [Details]
Dobbs, Neil (2007) 'Expanding cocycles for interval maps'. C. R. Math. Acad. Sci. Paris, 345 (1):39-44. Available Online [DOI] [Details]
Dobbs, Neil (2006) 'Hyperbolic dimension for interval maps'. Nonlinearity, 19 (12):2877-2894. Available Online [DOI] [Details]
                                                                                                                     

Research

Research Interests

Dynamical systems is the qualitative study of long-term behaviour of systems which evolve with time. My research is primarily in the field of real and complex one-dimensional dynamics, examining the rich geometric structures and ergodic properties of such systems. Questions such as dependence of Hausdorff dimension of Julia sets on parameters, existence of equlibrium states, dependence of equilibrium states on parameters are current topics of research.