Related papers: Transitive mappings on the Cantor fan
In this work, we develop shape expansions of minimal matchbox manifolds without holonomy, in terms of branched manifolds formed from their leaves. Our approach is based on the method of coding the holonomy groups for the foliated spaces, to…
We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…
We construct a family of partially hyperbolic skew-product diffeomorphisms on $\mathbb{T}^3$ that are robustly transitive and admitting two physical measures with intermingled basins. In particularly, all these diffeomorphisms are not…
We have established various criteria for the topological transitivity of families of continuous (holomorphic) functions. Furthermore, by leveraging the properties of expanding families of meromorphic functions, we offer an alternative proof…
It is known that if $f: \mathbb{S}^{1} \rightarrow \mathbb{S}^{1}$ is a transitive $C^{1+\alpha}$-local diffeomorphism non-invertible and non-uniformly expanding, then there is a unique parameter $t_{0} \in (0 , 1]$ such that the…
Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting…
Let $f$ be a chain mixing continuous onto mapping from the Cantor set onto itself.Let $g$ be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate $f$ in the topology of…
We show that every non-degenerate homogeneous plane continuum is homeomorphic to either the unit circle, the pseudo-arc, or the circle of pseudo-arcs. It follows that any planar homogenous compactum has the form $X \times Z$, where $X$ is a…
In this paper, we define a new notion of "freely tracing property by free chains" on $G$-like continua and we prove that a positive topological entropy homeomorphism on a $G$-like continuum admits a Cantor set $Z$ such that every tuple of…
The Kitaev magnets with bond-dependent interactions have garnered considerable attention in recent years for their ability to harbor exotic phases and nontrivial excitations. The topological magnons, which are indicated by nonzero Chern…
When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and…
We study magneto-transport through topological insulator nanowires shaped in the form of a constriction, as can be obtained by etching techniques. The magnetic field is coaxial, potentially turning the nanowire into a magneto-chiral…
It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex…
In the context of the Franks-Misiurewicz Conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class…
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve Rees construction, allowing to start with…
A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in…
Recently, considerable attention has been focused on the transformation optics and metamaterial due to their fascinating phenomena and potential applications. Concentrator is one of the most representative ones, which however is limited in…
We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…
We prove a reconstruction theorem valid for arbitrary theories in continuous (or classical) logic in a countable language, that is to say that we provide a complete bi-interpretation invariant for such theories, taking the form of an open…