On the Envelopes of Homotopies
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This paper is indented to explain a dynamics on homotopies on the compactmetric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes ofows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the flow geometry and the discrete geometry will be illustrated. In particular, it is shown that any ω-limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.
Abstract
This paper is indented to explain a dynamics on homotopies on the compactmetric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes ofows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the flow geometry and the discrete geometry will be illustrated. In particular, it is shown that any ω-limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.
참고문헌 (20)
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