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There are no piecewise linear maps of type |
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| Authors: | Ví ctor Jimé nez Ló pez L'ubomí r Snoha |
| Affiliation: | Departamento de Matemaaa ticas, Universidad de Murcia, Campus de Espinardo, Aptdo. de Correos 4021, 30100 Murcia, Spain ; Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banskaaa Bystrica, Slovakia |
| Abstract: | The aim of this paper is to show that there are no piecewise linear maps of type  . For this purpose we use the fact that any piecewise monotone map of type  has an infinite  -limit set which is a subset of a doubling period solenoid. Then we prove that piecewise linear maps cannot have any doubling period solenoids. |
| Keywords: | Asymptotically periodic point piecewise linear map piecewise monotone map solenoid wandering interval $omega $-limit set |
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