A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations
A continuum of path-dependent equilibrium solutions induced by sticky expectations
We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen...
A contribution to infinite disjoint covering systems
Let the collection of arithmetic sequences be a disjoint covering system of the integers. We prove that if for some primes and integers , then there is a such that . We conjecture that the divisibility result holds for all moduli.A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to . The above conjecture holds for saturated systems with such that the product of its prime factors is at most .
A convergence criterion for monotone global dynamical systems.
A convergence result and numerical study for a nonlinear piezoelectric material in a frictional contact process with a conductive foundation
We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky's law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed to be frictional, and the foundation is electrically conductive. The contact is modeled with the...
A convexity theorem for Poisson actions of compact Lie groups
A Cost-Effectiveness-Assessing Model of Vaccination for Varicella and Zoster
A decision analytical model is presented and analysed to assess the effectiveness and cost-effectiveness of routine vaccination against varicella and herpes-zoster, or shingles. These diseases have as common aetiological agent the varicella-zoster virus (VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity. The general concern is that universal varicella vaccination might lead to more cases of zoster: with more...
A counterexample to a Fedorenko statement.
A counterexample to a statement concerning Lyapunov stability.
A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas
We construct a two dimensional foliation with dense leaves on the Heisenberg nilmanifold for which smooth leafwise Hodge decomposition does not hold. It is also shown that a certain type of dynamical trace formulas relating periodic orbits with traces on leafwise cohomologies does not hold for arbitrary flows.
A criterion for potentially good reduction in nonarchimedean dynamics
Let K be a nonarchimedean field, and let ϕ ∈ K(z) be a polynomial or rational function of degree at least 2. We present a necessary and sufficient condition, involving only the fixed points of ϕ and their preimages, that determines whether or not the dynamical system ϕ: ℙ¹ → ℙ¹ has potentially good reduction.
A criterion for the non-existence of invariant circles
A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces
Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space model which...
A critical phenomenon in solitonic Ising chains.
A cut salad of cocycles
We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed.
A description of stochastic systems using chaotic maps.
A descriptive view of unitary group representations
In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if and are countable amenable non-type I groups, then the unitary duals of and are Borel isomorphic.
A deterministic discretisation-step upper bound for state estimation via Clark transformations.
A deterministic displacement theorem for Poisson processes.
A differential geometric setting for dynamic equivalence and dynamic linearization
This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.