Related papers: Non-typical points for $\beta$-shifts
Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial…
Determining the symmetry of the order parameter of unconventional superconductors remains a recurrent topic and non-trivial task in the field of strongly correlated electron systems. Here we show that the behavior of Dirac points away from…
Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce…
The well-known Jewett-Krieger's Theorem states that each ergodic system has a strictly ergodic model. Strengthening the model by requiring that it is strictly ergodic under some group actions, and building the connection of the new model…
Let $f$ be a rational function of degree $d>1$ on the projective line over a possibly non-archimedean algebraically closed field. A well-known process initiated by Brolin considers the pullbacks of points under iterates of $f$, and produces…
We study the sets DF({\beta}) of digit frequencies of {\beta}-expansions of numbers in [0,1]. We show that DF({\beta}) is a compact convex set with countably many extreme points which varies continuously with {\beta}; that there is a full…
Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behaviour of a system under parameter variation can differ…
Let f be a self-map of a compact manifold M, admitting an global SRB measure \mu. For a continuous test function \phi on M and a constant \alpha>0, consider the set of the initial points for which the Birkhoff time averages of the function…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
Exceptional points (EPs) are spectral defects displayed by non-Hermitian systems in which multiple degenerate eigenvalues share a single eigenvector. This distinctive feature makes systems exhibiting EPs more sensitive to external…
Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…
We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time…
We show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general…
Nonnesting permutations are permutations of the multiset $\{1,1,2,2,\dots,n,n\}$ that avoid subsequences of the form $abba$ for any $a\neq b$. These permutations have recently been studied in connection to noncrossing (also called…
For every $\beta\in(0,\infty)$, $\beta\neq 1$ we prove that a positive measure subset $A$ of the unit square contains a point $(x_0,y_0)$ such that $A$ nontrivially intersects curves $y-y_0 = a (x-x_0)^\beta$ for a whole interval…
New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are…
Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…
Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge -- a feature that was exploited for several applications. Here, we…
Invariant geodesic orbit Finsler $(\alpha,\beta)$ metrics $F$ which arise from Riemannian geodesic orbit metrics $\alpha$ on spheres are determined. The relation of Riemannian geodesic graphs with Finslerian geodesic graphs proved in a…
Non-conservative physical systems admit a special kind of spectral degeneracy, known as exceptional point (EP), at which eigenvalues and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. Dynamical parametric encircling…