Advanced SearchSearch Tips
On the Envelopes of Homotopies
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • 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;
  PDF(new window)
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 -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.
envelope;homotopies;-limit sets;
 Cited by
Chain Recurrences on Conservative Dynamics,;;

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

Kyungpook mathematical journal, 2014. vol.54. 2, pp.333-339 crossref(new window)
On the Omega Limit Sets for Analytic Flows, Kyungpook mathematical journal, 2014, 54, 2, 333  crossref(new windwow)
Chain Recurrences on Conservative Dynamics, Kyungpook mathematical journal, 2014, 54, 2, 165  crossref(new windwow)
A note on envelopes of homotopies, Journal of Difference Equations and Applications, 2015, 21, 6, 512  crossref(new windwow)
E. Akin, J. Auslander and K. Berg, Almost equicontinuity and the enveloping semigroup, Topological Dynamics and Applications, Contemporary Mathemat- ics (a volume in honor of R. Ellis), 215(1998), 75-81.

J. Auslander, Minimal ows and their extensions, Mathematics Studies 153., Notas de Matematica, 1988.

J. Auslander, S. Kolyada and L. Snoha, Functional envelope of a dynamical system, Nonlinearity, 20(2007), 2245-2269. crossref(new window)

C. Bonatti, S. Crovisier, G. Vago and A. Wilkinson, Local density of diffeomorphisms with large centralizers, arXiv:0709.4319.

H. -Y. Chu and J. Choy, On the dynamics of ows on compact metric spaces, To appear in Commun. Pur. Appl. Anal.

H. -Y. Chu and J. Choy, On attractors of analytic ows on $\mathbb{R}^2$, in preperation.

S. Donaldson and P. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs., Oxford Science Publications., The Clarendon Press, Oxford University Press, New York, 1990.

R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc., 94 (1960), 272-281. crossref(new window)

R. Ellis, The enveloping semigroup of projective ows, Ergodic Theory Dynam. Systems, 13 (1993), 635-660.

D. Ellis, R. Ellis and M. Nerurkar, The topological dynamics of semigroup actions, Trans. Amer. Math. Soc., 353 (2001) 1279-1320. crossref(new window)

R. Ellis and M. Nerurkar, Weakly almost periodic ows, Trans. Amer. Math. Soc., 313 (1989) 103-119. crossref(new window)

R. Friedman and J. Morgan, Smooth four-manifolds and complex surfaces, Springer-Verlag, (1994).

K. Fukaya, Floer homology for oriented three manifolds, In Aspects of low dimensional manifolds, ed. by Matsumoto, Morita., Advanced Studies in pure mathematics, 20 (1992) 1-92.

E. Glasner, Enveloping semigroups in topological dynamics, Topology and its Appl., 154 (2007) 2344-2363. crossref(new window)

J. Milnor, On the concept of attractor, Comm. Math. Phys., 99 (1985) 177-195. crossref(new window)

J. Milnor, On the concept of attractor: Correction and Remarks, Comm. Math. Phys., 102 (1985) 517-519. crossref(new window)

J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. Math., 60 (1965) 540-567.

S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967) 747-817. crossref(new window)

J. Vries, Elements of Topological Dynamics, Kluwer Academic Publishers, 1993.