𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Topological entropy for set valued maps

✍ Scribed by Marek Lampart; Peter Raith

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
272 KB
Volume
73
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

Any continuous map T on a compact metric space X induces in a natural way a continuous map T on the space K(X) of all non-empty compact subsets of X. Let T be a homeomorphism on the interval or on the circle. It is proved that the topological entropy of the induced set valued map T is zero or infinity. Moreover, the topological entropy of T | C(X) is zero, where C(X) denotes the space of all non-empty compact and connected subsets of X.

For general continuous maps on compact metric spaces these results are not valid.

πŸ“œ SIMILAR VOLUMES

Convexity for set-valued maps
Convexity for set-valued maps
✍ D. Kuroiwa πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 275 KB
Set-valued topological contractions
Set-valued topological contractions
✍ E. Tarafdar; X.-Z. Yuan πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 199 KB
Nash Equilibrium for Set-Valued Maps
Nash Equilibrium for Set-Valued Maps
✍ J. Guillerme πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 416 KB

We define a notion of Nash equilibrium for an arbitrary family of set-valued maps with values in pre-ordered sets. An existence theorem of such a Nash equilibrium is obtained from an intersection theorem for an arbitrary family of setvalued maps, generalizing results of Ky Fan, for example 1994 Acad

Set-valued stable maps
Set-valued stable maps
✍ A.V. Ostrovsky πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 94 KB

Various classes of maps (stable, transquotient, set-valued triquotient, harmonious, point-harmonious) are studied. It is proved that compositions of finitely many closed and open maps preserve consonance.