Related papers: Edrei's Conjecture revisited
Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the rotators are decoupled and we study the…
In this article we study conditions to be a continuous or a measurable eigenvalue of finite rank minimal Cantor systems, that is, systems given by an ordered Bratteli diagram with a bounded number of vertices per level. We prove that…
H. Lin and the author introduced the notion of approximate conjugacy of dynamical systems. In this paper, we will discuss the relationship between approximate conjugacy and full groups of Cantor minimal systems. An analogue of…
The Jacobian Conjecture states that any locally invertible polynomial system in C^n is globally invertible with polynomial inverse. C. W. Bass et al. (1982) proved a reduction theorem stating that the conjecture is true for any degree of…
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk…
We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows…
The aim of this paper is to study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. We use Bratteli diagrams to control invariant measures that are…
The paper is motivated by E. Akin's book about dynamical systems and closed relations [A], and by J. Kennedy's and G. Erceg's recent paper about the entropy of closed relations on closed intervals [EK]. In present paper, we introduce the…
In this paper, we completely solve the problem when a Cantor dynamical system $(X,f)$ can be embedded in $\mathbb{R}$ with vanishing derivative everywhere. For this purpose, we construct a refining sequence of marked clopen partitions of…
In this paper we prove four cases of the vanishing conjecture of differential operators with constant coefficients and also a conjecture on the Laurent polynomials with no holomorphic parts, which were proposed in [Zh3] by the third named…
We consider a recursive system $(X_n)$ which was introduced by Collet et al. [10] as a spin glass model, and later by Derrida, Hakim, and Vannimenus [13] and by Derrida and Retaux [14] as a simplified hierarchical renormalization model. The…
We prove ergodicity of unitary random-matrix theories by showing that the autocorrelation function with respect to energy or magnetic field strength of any observable vanishes asymptotically. We do so using Efetov's supersymmetry method, a…
The famous conjecture of V.Ya.Ivrii (1978) says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study the complex version of Ivrii's…
We show the Williams Conjecture is false for irreducible shifts of finite type by examining relative sign-gyration numbers of conjugacies between shifts with no points of period one or two.
Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is…
We are interested in the nearly supercritical regime in a family of max-type recursive models studied by Collet, Eckman, Glaser and Martin and by Derrida and Retaux, and prove that under a suitable integrability assumption on the initial…
In this paper we continue to explore infinitely renormalizable H\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with…
Chudnovsky, Scott, Seymour and Spirkl recently proved a conjecture by Kalai and Meshulam stating that the reduced Euler characteristic of the independence complex of a graph without induced cycles of length divisible by three is in…
A minimal Cantor system is said to be self-induced whenever it is conjugate to one of its induced systems. Substitution subshifts and some odometers are classical examples, and we show that these are the only examples in the equicontinuous…
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.