Related papers: Symbolic dynamics for non-uniformly hyperbolic sur…

Conventional momentum space provides an orientable base space of a torus for topological classifications based on band theory. Here, we introduce a non-orientable momentum space isomorphic to the real projective plane RP^2 within the…

The results of this paper are twofold: In the first part, we prove that for Schr\"odinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or…

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…

In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…

Disordered hyperuniform structures are an exotic state of matter having suppressed density fluctuations at large length-scale similar to perfect crystals and quasicrystals but without any long range orientational order. In the past decade,…

A polygonal surface in the pseudo-hyperbolic space H^(2,n) is a complete maximal surface bounded by a lightlike polygon in the Einstein universe Ein^(1,n) with finitely many vertices. In this article, we give several characterizations of…

We discuss asymptotically hyperbolic manifold with a noncompact boundary which is close to a horosphere in a certain sense. The model case is a horoball or the complement of a horoball in standard hyperbolic space. We show some geometric…

We prove that $\mathcal{C}^2$ surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of T.Downarowicz and A.Maass \cite{Dow} we bound the local…

We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…

Let $M_{\kappa }$ be the three-dimensional space form of constant curvature $\kappa =0,1,-1$, that is, Euclidean space $\mathbb{R}^{3}$, the sphere $S^{3} $, or hyperbolic space $H^{3}$. Let $S$ be a smooth, closed, strictly convex surface…

Given a locally maximal compact invariant hyperbolic set $\Lambda$ for a $C^1$ flow or diffeomorphism on a Riemann manifold with $C^1$ unstable laminations, we construct an invariant continuous bundle of tangent vectors to local unstable…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

Let Diff^1(M) be the set of all C^1-diffeomorphisms f : M \rightarrow M, where M is a compact boundaryless d-dimensional manifold, d \geq 2. We prove that there is a residual subset R of Diff^1(M) such that if f \in R and if H(p) is the…

In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

This paper concerns with deformations of noncompact complex hyperbolic manifolds (with locally Bergman metric), varieties of discrete representations of their fundamental groups into $PU(n,1)$ and the problem of (quasiconformal) stability…

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…

Outer Billiards is a geometrically inspired dynamical system based on a convex shape in the plane. When the shape is a polygon, the system has a combinatorial flavor. In the polygonal case, there is a natural acceleration of the map, a…

We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in…

Motivated by an experimental study of groups generated by reflections in planar patterns of tangent circles, we describe some methods for constructing and studying representation spaces of holonomy groups of infinite volume hyperbolic…