On the Envelopes of Homotopies

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 3,  2009, pp.573-582
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.3.573
Title & Authors
On the Envelopes of Homotopies
Choyy, Jae-Yoo; Chu, Hahng-Yun;

Abstract
This paper is indented to explain a dynamics on homotopies on the compact metric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes of flows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the ow geometry and the discrete geometry will be illustrated. In particular, it is shown that any $\small{{\omega}}$-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.
Keywords
envelope;homotopies;$\small{{\omega}}$-limit sets;
Language
English
Cited by
1.
Chain Recurrences on Conservative Dynamics,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.165-171
2.
On the Omega Limit Sets for Analytic Flows,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.333-339
1.
On the Omega Limit Sets for Analytic Flows, Kyungpook mathematical journal, 2014, 54, 2, 333
2.
Chain Recurrences on Conservative Dynamics, Kyungpook mathematical journal, 2014, 54, 2, 165
3.
A note on envelopes of homotopies, Journal of Difference Equations and Applications, 2015, 21, 6, 512
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