Homology and chaotic unfolding of chaos manifolds
Section snippets
Introduction and definitions
The folding of a manifold was, firstly introduced by Roberston in 1977 [16], while the chaotic unfolding of a manifold appeared in 1985 [23]. Since then many authors have studied the folding of manifolds such as in [17], [18], [19], [20], [21], [22], [23]. The related homology group of manifolds were discussed in [1], [2], [3], [5], [8], [9], [10], [11], [12], [14], [15]. And for manifolds without boundaries, this homology groups were explained in [4], [6], [7], [13], in our article we define
Conclusions and some applications
In quantum mechanics some problems deals with manifold solved analytically, but many problems in quantum mechanics discussed with algebraic technic. This article gives the relation between the homology group of manifold and homology of its unfolding in the two cases. When the boundary preserved and in the case of variant this boundary in chaos manifold (represented as the perterpation of the orbits of the atoms during the effect of a magnetic field and suddenly make a boundary of this magnetic
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