In this work, we show that a strongly continuous semigroup generated by a normal operator N is conjugate to the semigroup generated by the real part of N , provided zero is not an eigenvalue of the real part of N . We also show that in case N satisfies a certain sectorial property, the homeomorphism establishing the conjugacy, as well as its inverse, is locally Hölder continuous. Moreover, in c...

This answers a question apparently first raised by Tietze [T, p. 83]. It was previously known that there were at most two knots with a given complement [CGLS, Corollary 3]. The notion of equivalence of knots can be strengthened by saying that K and K' are isotopic if the above homeomorphism h is isotopic to the identity, or, equivalently, orientation-preserving. The analog of Theorem I holds in...

In this paper, the global asymptotic stability of second-order neutral type Cohen-Grossberg neural networks with time-varying delays are investigated. First, by choosing properly variable substitution the system is transformed to first-order differential equation. Second, some sufficient conditions which can ensure the existence and global asymptotic stability of equilibrium point for the syste...

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another application we giv...

We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ , which was started in [B-K 1], [B-D-K 1; 2], [B-D-M], and [M]. We prove that the set of periodic homeomorphisms is τ -dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), τ) has the Rokhlin property, i.e., there exists a...

In this paper, the abstract computational principles underlying topographic maps are discussed. We give a definition of a “perfectly neighbourhood preserving” map, which we call a topographic homeomorphism, and we prove that this has certain desirable properties. It is argued that when a topographic homeomorphism does not exist (the usual case), many equally valid choices are available for quan...

We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere — i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if Ḡ is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in Ḡ, then Ḡ has a...

Using holomorphic surgery techniques, we construct a homeomorphism between a neighborhood of any limb without root point of the Mandelbrot set and a neighborhood of any other of equal denominator, in such a way that the limbs are mapped to each other. On the limbs, the homeomorphism coincides with that constructed in “Homeomorphisms between limbs of the Mandelbrot set” (J. Geom. Anal. 9 (1999),...

A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to ∂M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in ∂M . In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and ∂M is a single torus, an...

Abstract We completely determine finite abelian regular branched covers of the 2-sphere $S^{2}$ with property that each homeomorphism preserving branching set can be lifted.