This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works on well chosen examples (see e.g. citeGamb-dif) show that the dynamical behaviours of dynamical systems and of their discretizations can be quite different. ...

An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

In this article, we introduce the concept of neutrosophic e-open and e-closed mappings in topological spaces studied some their related properties. Further work is extended to e-homeomorphism, e-Completely homeomorphism eT12-space establishes attributes.

In 1990, M. Barge and J. Martin [BM90] proved that the shift map on the inverse limit space ([0, 1], f), for any map f : [0, 1]→ [0, 1], can be realized as a global attractor in the plane. In 1960, M. Brown [Bro60] proved that the inverse limit space of any near homeomorphism (Definition 1.2) of a compact metric space is homeomorphic to the original space. M. Barge and J. Martin prove that, for...

We study several natural classes and relations occurring in continuum theory from the viewpoint of descriptive set theory and infinite combinatorics. We provide useful characterizations for the relation of likeness among dendrites and show that it is a bqo with countably many equivalence classes. For dendrites with finitely many branch points the classes of homeomorphism and quasi-homeomorphism...

Let P = fp1; : : : ; png and Q = fq1; : : : ; qng be two point sets lying in the interior of rectangles in the plane. We show how to construct a piecewise linear homeomorphism of size O(n2) between the rectangles which maps pi to qi for each i. This bound is optimal in the worst case; i.e., there exist point sets for which any piecewise linear homeomorphism has size (n2). Introduction A homeomo...

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Given two undirected trees T and P , the Subtree Homeomorphism Problem is to find whether T has a subtree t that can be transformed into P by removing entire subtrees, as well as repeatedly removing a degree-2 node and adding the edge joining its two neighbors. In this paper we extend the Subtree Homeomorphism Problem to a new optimization problem by enriching the subtree-comparison with node-t...