Bo Ju Jiang applied Neilsen theory to the study of periodic orbits of a homeomorphism. His method employs a certain loop in the mapping torus of the homeomorphism. Our interest concerns the persistence of periodic orbits in parameterized families of homeomorphisms. This leads us to consider fibre bundles and equivariant maps, which gives us a nice point of view.

We investigate the end spaces of infinite dual graphs. We show that there exists a natural homeomorphism between the end spaces of a graph and its dual, and that this homeomorphism maps thick ends to thick ends. Along the way, we prove that Tutte-connectivity is invariant under taking

This paper is concerned with fuzzy cellular neural networks with distributed delays. Sufficient conditions on the existence, uniqueness and global exponential stability of equilibrium point are established by using the Homeomorphism theory and applying elementary inequality 2ab ≤ a2 + b2. Moreover an example is given to illustrate results obtained. Key–Words: Fuzzy cellular neural networks, Glo...

Let f be an orientation preserving homeomorphism of the disc D which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2π/3 or 4π/3, or J has a periodic point of least period n for each n ∈ N∗.

In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudocovering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus 2 admits an expansive homeomorphism.

Let T be a tent map with the slope strictly between √ 2 and 2. Suppose that the critical point of T is not recurrent. Let K denote the inverse limit space obtained by using T repeatedly as the bonding map. We prove that every homeomorphism of K to itself is isotopic to some power of the natural shift homeomorphism.

We propose a relaxed notion of shadowing. In particular, for homeomorphism f on metric space, we ask whether every approximate orbit is near some actual nearby system. distinguish the cases where close or arbitrarily to f. prove relations between these notions and ordinary shadowing present various examples. finally discuss an application, $$C^0$$ -closing lemma chain recurrent points topologic...