Related papers: Discrepancy Properties and Conjugacy Classes of In…
We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with $\beta > 2$ having the property that the orbit of 0 is bounded away from 1.
In this paper, various chaotic properties and their relationships for interval maps are discussed. It is shown that the proximal relation is an equivalence relation for any zero entropy interval map. The structure of the set of…
We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $\Psi -\Psi\circ T=\Phi$ has a bounded solution $\Psi$ provided that the datum $\Phi$ belongs to a finite codimension…
We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in…
(abridged) The {stellar IMF} has been found to be essentially invariant. While some apparent differences are seen, the uncertainties inherent to this game do not allow a firm conclusion to be made that the IMF varies systematically with…
Let $d >1$. In this paper we show that for an irreducible permutation $\pi$ which is not a rotation, the set of $[\lambda]\in \mathbb{P}_+^{d-1}$ such that the interval exchange transformation $f([\lambda],\pi)$ is not weakly mixing does…
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random…
It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…
Orbital degrees of freedom shape many of the properties of a wide class of Mott insulating, transition metal oxides with partially filled 3d-shells. Here we study orbital ordering transitions in systems where a single electron occupies the…
We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the…
A recently developed semiclassical approximation to exchange in one dimension is shown to be almost exact, with essentially no computational cost. The variational stability of this approximation is tested, and its far greater accuracy…
We have recently presented strong evidence that chaotic orbits that obey one isolating integral besides energy exist in a toy Hamiltonian model with three degrees of freedom and are bounded by regular orbits that isolate them from the…
Superexchange calculation is performed for multi-orbital band models with broken inversion symmetry. Orbital-changing hopping terms allowed by the symmetry breaking electric field lead to a new kind of orbital exchange term closely…
The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…
Given a feature set for the shape of a closed loop, it is natural to ask which features in that set do not change when the starting point of the path is moved. For example, in two dimensions, the area enclosed by the path does not depend on…
In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a…
We study discontinuous interval maps generated by the action of erasing block substitutions on the binary expansion. After establishing some general properties of these maps, we categorize erasing block substitutions in a hierarchy of…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the…
Using Monte Carlo and analytic techniques, we study a minimal dynamic network involving two populations of nodes, characterized by different preferred degrees. Reminiscent of introverts and extroverts in a population, one set of nodes,…