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Quasistatic dynamical systems
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 inExpand
Approximation algorithms for the joint replenishment problem with deadlines
TLDR
The Joint Replenishment Problem ($${\hbox {JRP}}$$JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods from a supplier to retailers. Expand
Measures with positive Lyapunov exponent and conformal measures in rational dynamics
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 areExpand
On cusps and flat tops
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 notExpand
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 aExpand
Visible measures of maximal entropy in dimension one
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
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 haveExpand
Diabolical Entropy
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 theExpand
Approximation Algorithms for the Joint Replenishment Problem with Deadlines
TLDR
The Joint Replenishment Problem is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods over time from a supplier to retailers. Expand
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