Piecewise linear interval maps both expanding and contracting

2000 ◽  
Vol 15 (4) ◽  
pp. 343-351 ◽  
Author(s):  
Moses A. Boudourides ◽  
Nikos A. Fotiades
Keyword(s):  
Piecewise Linear ◽  
Interval Maps ◽  
Linear Interval

scholarly journals Topological conjugacies of piecewise monotone interval maps

2001 ◽  
Vol 25 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Nikos A. Fotiades ◽  
Moses A. Boudourides
Keyword(s):  
Topological Entropy ◽  
Piecewise Linear ◽  
Topological Conjugacy ◽  
Markov Condition ◽  
Piecewise Monotone ◽  
Interval Maps ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Topological Conjugacies

Our aim is to establish the topological conjugacy between piecewise monotone expansive interval maps and piecewise linear maps. First, we are concerned with maps satisfying a Markov condition and next with those admitting a certain countable partition. Finally, we compute the topological entropy in the Markov case.

scholarly journals Spaces of transitive interval maps

2014 ◽  
Vol 35 (7) ◽  
pp. 2151-2170 ◽  
Author(s):  
SERGIĬ KOLYADA ◽  
MICHAŁ MISIUREWICZ ◽  
L’UBOMÍR SNOHA
Keyword(s):  
Piecewise Linear ◽  
Real Interval ◽  
Piecewise Monotone ◽  
Interval Maps ◽  
Arcwise Connected

On a compact real interval, the spaces of all transitive maps, all piecewise monotone transitive maps and all piecewise linear transitive maps are considered with the uniform metric. It is proved that they are contractible and uniformly locally arcwise connected. Then the spaces of all piecewise monotone transitive maps with given number of pieces as well as various unions of such spaces are considered and their connectedness properties are studied.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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