Extending maps of a Cantor set product with an arc to near homeomorphisms of the 2-disk

Authors
Sanford, MD Walker, RB
Citation
Md. Sanford et Rb. Walker, Extending maps of a Cantor set product with an arc to near homeomorphisms of the 2-disk, PAC J MATH, 192(2), 2000, pp. 369-384
Citations number
13
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
192
Issue
2
Year of publication
2000
Pages
369 - 384
Database
ISI
SICI code
0030-8730(200002)192:2<369:EMOACS>2.0.ZU;2-M
Abstract
We prove that a positive entropy map of the product of a Cantor Set and an arc (which covers a homeomorphism) cannot be "embedded" into a near homeomo rphism of the 2-disk. Thus a theorem of M. Brown cannot be used to embed th e induced shift map on the corresponding inverse limit space into a 2-disk homeomorphism.