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Spaces of transitive interval maps

Published online by Cambridge University Press:  05 August 2014

SERGIĬ KOLYADA ,
MICHAŁ MISIUREWICZ  and
L’UBOMÍR SNOHA
SERGIĬ KOLYADA
Affiliation:
Institute of Mathematics, NASU, Tereshchenkivs’ka 3, 01601 Kiev, Ukraine email skolyada@imath.kiev.ua
MICHAŁ MISIUREWICZ
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202, USA email mmisiure@math.iupui.edu
L’UBOMÍR SNOHA
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Lubomir.Snoha@umb.sk
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2151 - 2170
Copyright
© Cambridge University Press, 2014 

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