A centerpiece of Dynamical Systems is comparison by an equivalence relationship called topological conjugacy. Current state of the field is that, generally, there is no easy way to determine if two systems are conjugate or to explicitly find the conjugacy between systems that are known to be equivalent. We present a new and highly generalizable method to produce conjugacy functions based on a f...

On closed orientable 3-manifolds, we consider a class $$ \mathcal{G} of homeomorphisms such that the nonwandering set each f ∈ is finite union surfaces restriction some power fk on these pseudo-Anosov homeomorphism. We prove exist only 3-manifolds form Sg × ℝ/(J(z),r−1), where J : → either homeomorphism surface genus g > 1 or periodic commuting with manifold, construct model and find necessary ...

We compute the polynomial entropy of induced maps on hyperspace for a homeomorphism $f$ an interval or circle with finitely many non-wandering points.

The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in number ways, including as colimit homeomorphism groups with given compact support, or subgroup the its Stone-\v{C}ech compactification. A is said to have Compactly Supported Homeomorphism Property (CSHP) if these two topologies coincide. authors provide necessary and sufficient conditions for finite produ...

Abstract We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains ( Y , d ). say that a metric space ) is domain if completion ? of has finite Hausdorff 2-measure, boundary ? = \ homeomorphic ???? 1 and there exists homeomorphism ? : ???? ?( in geometric sense. show continuous, monotone, surjective ?: ? ?. This result best possible this generality. In addition, we...

We give a short proof of Waldhausen’s homeomorphism theorem for orientable Haken manifolds. We give here a short proof of Waldhausen’s homeomorphism theorem [4] for orientable Haken manifolds. Recall that a compact irreducible 3-manifold is Haken (i.e., it has a hierarchy) if and only if it is sufficiently large (i.e., it admits an incompressible surface). This follows from the Haken-Kneser arg...

We classify, up to homeomorphism, all closed manifolds having the homotopy type of a connected sum of two copies of real projective n-space. 1. Statement of results Let P = Pn(R) be real projective n-space. López de Medrano [LdM71] and C.T.C. Wall [Wal68, Wal99] classified, up to PL homeomorphism, all closed PL manifolds homotopy equivalent to P when n > 4. This was extended to the topological ...