Towards the complete classification of tent maps inverse limits

Iztok Banič (Author), Matevž Črepnjak (Author), Matej Merhar (Author), Uroš Milutinović (Author)

Abstract

We study tent map inverse limits, i.e. inverse limits of inverse sequences of unit segments ▫$I$▫ with a tent map being the only bonding function. As the main result we identify an infinite family of curves in ▫$I^2$▫ such that if top points of graphs of tent maps belong to the same curve, the corresponding inverse limits are homeomorphic, and if they belong to different curves, the inverse limits are non-homeomorphic. The inverse limits corresponding to certain families of top points are explicitly determined, and certain properties of the inverse limit are proved in the case of ▫$(0,1)$▫ as the top point.

Keywords

matematika;topologija;kontinuumi;inverzne limite;mathematics;topology;continua;inverse limits;tent maps;Knaster continua;

Data

Language:	English
Year of publishing:	2010
Typology:	0 - Not set
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	515.126
COBISS:	15633497
ISSN:	2232-2094
Parent publication:	Preprint series
Views:	38
Downloads:	9
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	matematika;topologija;kontinuumi;inverzne limite;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-24
Volume:	ǂVol. ǂ48
Issue:	ǂšt. ǂ1124
Chronology:	2010
ID:	68482