Barycentric extensions of monotone maps of the circle

2004 ◽  
pp. 1-20 ◽  
Author(s):  
William Abikoff ◽  
Clifford J. Earle ◽  
Sudeb Mitra
Keyword(s):  
Monotone Maps

scholarly journals Monotone maps on dendrites and their induced maps

2016 ◽  
Vol 204 ◽  
pp. 121-134 ◽  
Author(s):  
Haithem Abouda ◽  
Issam Naghmouchi
Keyword(s):  
Monotone Maps ◽  
Induced Maps

scholarly journals Monotone maps, the likeness relation and G-structures

2008 ◽  
Vol 155 (17-18) ◽  
pp. 2031-2040
Author(s):  
Daniel Cichoń ◽  
Paweł Krupski ◽  
Krzysztof Omiljanowski
Keyword(s):  
Monotone Maps

ESSENTIAL ENTROPY-CARRYING HORSESHOES AS SET LIMITS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250195 ◽  
Author(s):  
STEVEN M. PEDERSON
Keyword(s):  
Topological Entropy ◽  
Convergent Sequence ◽  
Invariant Set ◽  
Invariant Sets ◽  
Piecewise Monotone ◽  
Interval Maps ◽  
Monotone Map ◽  
Monotone Maps

This paper studies the set limit of a sequence of invariant sets corresponding to a convergent sequence of piecewise monotone interval maps. To do this, the notion of essential entropy-carrying set is introduced. A piecewise monotone map f with an essential entropy-carrying horseshoe S(f) and a sequence of piecewise monotone maps [Formula: see text] converging to f is considered. It is proven that if each gi has an invariant set T(gi) with at least as much topological entropy as f, then the set limit of [Formula: see text] contains S(f).

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