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.
A dimension group for local homeomorphisms and endomorphisms of onesided shifts fo finite type.
A direct proof of a theorem by Kolmogorov in hamiltonian systems
A discrete heterogeneous-group economic growth model with endogenous leisure time.
A discrete variational approach for investigation of stationary localized states in a discrete nonlinear Schrödinger equation, named IN-DNLS.
A discrete-continuous model for bisexual population dynamics.
A discretization of the nonholonomic Chaplygin sphere problem.
A distributionally chaotic triangular map with zero sequence topological entropy.
A dual approach to triangle sequences: a multidimensional continued fraction algorithm.
A dynamic economic model with discrete time and consumer sentiment.
A dynamical interpretation of the global canonical height on an elliptic curve.
A dynamical invariant for Sierpiński cardioid Julia sets
For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located in the parameter...
A dynamical Shafarevich theorem for twists of rational morphisms
Let K denote a number field, S a finite set of places of K, and ϕ: ℙⁿ → ℙⁿ a rational morphism defined over K. The main result of this paper states that there are only finitely many twists of ϕ defined over K which have good reduction at all places outside S. This answers a question of Silverman in the affirmative.
A dynamical system connected with inhomogeneous 6-vertex model