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Quasistatic dynamical systems

- N. Dobbs, Mikko Stenlund
- Mathematics, Physics
- Ergodic Theory and Dynamical Systems
- 8 April 2015

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in… Expand

Approximation algorithms for the joint replenishment problem with deadlines

- M. Bienkowski, J. Byrka, +5 authors N. Young
- Mathematics, Computer Science
- J. Sched.
- 13 December 2012

TLDR

Measures with positive Lyapunov exponent and conformal measures in rational dynamics

- N. Dobbs
- Mathematics
- 23 April 2008

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 measures are… Expand

On cusps and flat tops

- N. Dobbs
- Mathematics
- 24 January 2008

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 $C^{1+\epsilon}$. We do not… Expand

Nice sets and invariant densities in complex dynamics

- N. Dobbs
- Mathematics
- Mathematical Proceedings of the Cambridge…
- 18 February 2009

Abstract In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a… Expand

Visible measures of maximal entropy in dimension one

- N. Dobbs
- Mathematics
- 1 June 2007

A real one-dimensional analogue of Zdunik’s dichotomy is proven giving dynamical conditions for a multimodal map to have a measure of maximal entropy of dimension one.

Free energy jumps up

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 upper-semicontinuous:… Expand

Hyperbolic dimension for interval maps

- N. Dobbs
- Mathematics
- 2 November 2006

The hyperbolic and Hausdorff dimensions are shown to coincide for C2 maps without recurrent critical points. The maps may have parabolic periodic points. The Julia set for certain such maps may have… Expand

Diabolical Entropy

- N. Dobbs, N. Mihalache
- Mathematics
- 8 October 2016

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 precise formula for the… Expand

Approximation Algorithms for the Joint Replenishment Problem with Deadlines

- M. Bienkowski, J. Byrka, +5 authors Neal E. Young
- Mathematics, Computer Science
- ICALP
- 8 July 2013

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