2. A topological classification of the almost periodic homeomorphisms on a closed 2-cell. A homeomorphism A of a metric space (X, p) onto itself is said to be almost periodic on X if €>0 implies that there exists a relatively dense sequence {«¿} of integers such that p(x, A"*'(x)) <e for all xGA and i= ±1, ±2, • • •. A homeomorphism A of the space X onto itself is said to be topologically equiv...

This paper extends the edge addition planarity algorithm from Boyer and Myrvold to provide a new way of solving the subgraph homeomorphism problem for K2,3, K4, and K3,3. These extensions derive much of their behavior and correctness from the edge addition planarity algorithm, providing an alternative perspective on these subgraph homeomorphism problems based on affinity with planarity rather t...

We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a punctured sphere. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured disk together with a homomorphism to the integers. The technique, following Ivanov, is to prove that every superinjective map of the com...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. The aim of the paper is to study the homeomorphism classes of decomposable trees. More precisely, we show that homeomorphism classes containing decomposable trees with an arbitrarily large minimal dist...

We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in particular, that the nonwandering set is weakly transitive. We give an example showing that the nonwandering set of such a homeomorphism may not be transitive.

We consider the homeomorphism problem for countable topological spaces and investigate its descriptive complexity as an equivalence relation. It is shown that even for countable metric spaces the homeomorphism problem is strictly more complicated than the isomorphism problem for countable graphs and indeed it is not Borel reducible to any orbit equivalence relation induced by a Borel action of ...

Xiong proved that if f : I ! I is any map of the unit interval I , then the depth of the centre of f is at most 2, and Ye proved that for any map f : T ! T of a finite tree T , the depth of the centre of f is at most 3. It is natural to ask whether the result can be generalized to maps of dendrites. In this note, we show that there is a dendrite D such that for any countable ordinal number 1⁄2 ...

The aim of this paper is to obtain nonlinear operators in suitable function spaces whose fixed points coincide with the solutions of the nonlinear boundary value problems (φ(u)) = f(t, u, u), l(u, u) = 0, where l(u, u) = 0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T ], φ : R → R is a suitable monotone homeomorphism and f : [0, T ]× R × R → R is a Carathéodory functio...

1. Summary. In Part I, we develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and...

Tree pattern matching is a fundamental problem that has a wide range of applications in Web data management, XML processing, and selective data dissemination. In this paper we develop efficient algorithms for the tree homeomorphism problem, i.e., the problem of matching a tree pattern with exclusively transitive (descendant) edges. We first prove that deciding whether there is a tree homeomorph...